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0)"],"region_exact":{},"oeis_ids":["A034870"],"derivation":{"root":"n-08f49539099949d5","steps":[],"edges":[],"text":"A034870"},"headline":"A034870: Even-numbered rows of Pascal's triangle.","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:          16,            32,             16;\n  2:         256,          1024,           1536,           1024,             256;\n  3:        4096,         24576,          61440,          81920,           61440,           24576,             4096;\n  4:       65536,        524288,        1835008,        3670016,         4587520,         3670016,          1835008,           524288,            65536;\n  5:     1048576,      10485760,       47185920,      125829120,       220200960,       264241152,        220200960,        125829120,         47185920,         10485760,          1048576;\n  6:    16777216,     201326592,     1107296256,     3690987520,      8304721920,     13287555072,      15502147584,      13287555072,       8304721920,       3690987520,       1107296256,        201326592,         16777216;\n  7:   268435456,    3758096384,    24427626496,    97710505984,    268703891456,    537407782912,     806111674368,     921270484992,     806111674368,     537407782912,     268703891456,      97710505984,      24427626496,      3758096384,       268435456;\n  8:  4294967296,   68719476736,   515396075520,  2405181685760,   7816840478720,  18760417148928,   34394098106368,   49134425866240,   55276229099520,   49134425866240,   34394098106368,   18760417148928,    7816840478720,   2405181685760,    515396075520,    68719476736,     4294967296;\n  9: 68719476736, 1236950581248, 10514079940608, 56075093016576, 210281598812160, 588788476674048, 1275708366127104, 2186928627646464, 3007026863013888, 3341140958904320, 3007026863013888, 2186928627646464, 1275708366127104, 588788476674048, 210281598812160, 56075093016576, 10514079940608, 1236950581248, 68719476736;\n","recurrence_sentence":"The row polynomials satisfy P(n,x) = (16+32*x+16*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[(16 + 32*x + 16*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] = (16 + 32*x + 16*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-08f49539099949d5","steps":["basis A013609","basis A013609"],"edges":["e-9638204c7017296b","e-21b9838b2d2dd4bd"],"text":"A034870 \u2192 basis A013609 \u2192 basis A013609"},"headline":"A034870 \u2192 basis A013609 \u2192 basis A013609","chain":null}