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0]"],"region_exact":{},"oeis_ids":[],"derivation":{"root":"n-336459bdce627a87","steps":["basis A013609"],"edges":["e-65b163cdbb61d2ab"],"text":"A139548 \u2192 basis A013609"},"headline":"A139548 \u2192 basis A013609","chain":null}}],"oeis":[],"bfiles":[],"oeis_texts":[{"oeis_id":"","target":"node","first_row":0,"oeis_offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false,"rows_shown":10,"polytool_commit":"c48629374597092cc41ef4d6273f37991516f984","triangle_example":"Triangle begins:\n  0:              1;\n  1:             32,              64,               32;\n  2:           1024,            4096,             6144,              4096,               1024;\n  3:          32768,          196608,           491520,            655360,             491520,             196608,              32768;\n  4:        1048576,         8388608,         29360128,          58720256,           73400320,           58720256,           29360128,             8388608,             1048576;\n  5:       33554432,       335544320,       1509949440,        4026531840,         7046430720,         8455716864,         7046430720,          4026531840,          1509949440,           335544320,            33554432;\n  6:     1073741824,     12884901888,      70866960384,      236223201280,       531502202880,       850403524608,       992137445376,        850403524608,        531502202880,        236223201280,         70866960384,         12884901888,         1073741824;\n  7:    34359738368,    481036337152,    3126736191488,    12506944765952,     34394098106368,     68788196212736,    103182294319104,     117922622078976,     103182294319104,      68788196212736,      34394098106368,      12506944765952,      3126736191488,       481036337152,        34359738368;\n  8:  1099511627776,  17592186044416,  131941395333120,   615726511554560,   2001111162552320,   4802666790125568,   8804889115230208,   12578413021757440,   14150714649477120,   12578413021757440,    8804889115230208,    4802666790125568,   2001111162552320,    615726511554560,    131941395333120,    17592186044416,    1099511627776;\n  9: 35184372088832, 633318697598976, 5383208929591296, 28710447624486912, 107664178591825920, 301459700057112576, 653162683457077248, 1119707457354989568, 1539597753863110656, 1710664170959011840, 1539597753863110656, 1119707457354989568, 653162683457077248, 301459700057112576, 107664178591825920, 28710447624486912, 5383208929591296, 633318697598976, 35184372088832;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (32+64*x+32*x^2)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[(32 + 64*x + 32*x^2)*P[n - 1, x]];\nTable[CoefficientList[P[n, x], x], {n, 0, 9}] // Flatten","pari":"P(N) = {my(v = vector(N + 1)); v[1] = 1; for(n = 1, N, my(i = n + 1); v[i] = (32 + 64*x + 32*x^2)*v[i - 1]); v};\nrow(n, p) = {my(c = Vecrev(p)); c};\nT(N) = {my(v = P(N)); concat(vector(#v, i, row(i - 1, v[i])))};\nT(9)","reading":{"first_row":0,"offset":0,"reversed":false,"trim_zeros":"none","regular_triangle":false}}],"derivation":{"root":"n-336459bdce627a87","steps":["basis A013609","basis A013609"],"edges":["e-65b163cdbb61d2ab","e-72273447476c7c97"],"text":"A139548 \u2192 basis A013609 \u2192 basis A013609"},"headline":"A139548 \u2192 basis A013609 \u2192 basis A013609","chain":null}