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(\u03b8+1)\u00b2","chain":null}},{"id":"l-3dbdd1001e51642c","kind":"oeis_match","node_a_id":"n-05cda65b61f08ead","node_b_id":null,"fingerprint":null,"oeis_id":"A228310","in_catalog":0,"target":"row_sums","row_alignment":null,"rows_matched":null,"oeis_nonn":1,"details":{"alignment":{"first_row":1,"low_zeros_dropped":false,"oeis_offset":2,"oeis_term_position":0,"target":"row_sums","terms_compared":14},"in_catalog":false,"oeis_id":"A228310","oeis_nonn":true},"other_id":null,"other":null}],"oeis":[{"oeis_id":"A228310","relation":"match_row_sums"}],"bfiles":[{"node_id":"n-05cda65b61f08ead","oeis_id":"A228310","target":"row_sums","oeis_offset":2,"first_row":1,"rows_used":200,"terms_matched":14,"oeis_terms_agreeing":22,"oeis_terms_available":22,"term_count":200,"raw_size":13733}],"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:   2,     8;\n  2:   4,    32,     36;\n  3:   8,    96,    216,    128;\n  4:  16,   256,    864,   1024,     400;\n  5:  32,   640,   2880,   5120,    4000,    1152;\n  6:  64,  1536,   8640,  20480,   24000,   13824,    3136;\n  7: 128,  3584,  24192,  71680,  112000,   96768,   43904,    8192;\n  8: 256,  8192,  64512, 229376,  448000,  516096,  351232,  131072,  20736;\n  9: 512, 18432, 165888, 688128, 1612800, 2322432, 2107392, 1179648, 373248, 51200;\n","recurrence_sentence":"The row polynomials satisfy (1+(3*n-1)*x+n^2*x^2)*P(n,x) = (2+(6*n+6)*x+(2*n^2+10*n+6)*x^2+(2*n^2+4*n+2)*x^3)*P(n-1,x) for n >= 1, with P(0,x) = 1.","mathematica":"P[0, x_] := 1;\nP[n_, x_] := P[n, x] = Expand[Together[((2 + (6*n + 6)*x + (2*n^2 + 10*n + 6)*x^2 + (2*n^2 + 4*n + 2)*x^3)*P[n - 1, x])/(1 + (3*n - 1)*x + n^2*x^2)]];\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] = ((2 + (6*n + 6)*x + (2*n^2 + 10*n + 6)*x^2 + (2*n^2 + 4*n + 2)*x^3)*v[i - 1])/(1 + (3*n - 1)*x + n^2*x^2)); 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-d28ad9841fc73317","steps":["(\u03b8+1)\u00b2"],"edges":["e-30a80ba9b1383179"],"text":"A038208 \u2192 (\u03b8+1)\u00b2"},"headline":"A038208 \u2192 (\u03b8+1)\u00b2","chain":null}