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2).","chain":null}},{"id":"l-aa1ba662d560047a","kind":"oeis_match","node_a_id":"n-5079b06e19e537fc","node_b_id":null,"fingerprint":null,"oeis_id":"A040075","in_catalog":0,"target":"row_sums","row_alignment":null,"rows_matched":null,"oeis_nonn":1,"details":{"alignment":{"first_row":0,"low_zeros_dropped":false,"oeis_offset":0,"oeis_term_position":0,"target":"row_sums","terms_compared":15},"in_catalog":false,"oeis_id":"A040075","oeis_nonn":true},"other_id":null,"other":null}],"oeis":[{"oeis_id":"A040075","relation":"match_row_sums"}],"bfiles":[{"node_id":"n-5079b06e19e537fc","oeis_id":"A040075","target":"row_sums","oeis_offset":0,"first_row":0,"rows_used":200,"terms_matched":15,"oeis_terms_agreeing":22,"oeis_terms_available":22,"term_count":200,"raw_size":14209}],"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:     10,      10;\n  2:     60,     120,       60;\n  3:    280,     840,      840,      280;\n  4:   1120,    4480,     6720,     4480,     1120;\n  5:   4032,   20160,    40320,    40320,    20160,     4032;\n  6:  13440,   80640,   201600,   268800,   201600,    80640,    13440;\n  7:  42240,  295680,   887040,  1478400,  1478400,   887040,   295680,    42240;\n  8: 126720, 1013760,  3548160,  7096320,  8870400,  7096320,  3548160,  1013760,  126720;\n  9: 366080, 3294720, 13178880, 30750720, 46126080, 46126080, 30750720, 13178880, 3294720, 366080;\n","recurrence_sentence":"The row polynomials satisfy n*P(n,x) = (2*n+8+(2*n+8)*x)*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*n + 8 + (2*n + 8)*x)*P[n - 1, x])/(n)]];\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*n + 8 + (2*n + 8)*x)*v[i - 1])/(n)); 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-79986ab5023c2764","steps":["basis A013609"],"edges":["e-7c97406b114f1661"],"text":"A178821 \u2192 basis A013609"},"headline":"A178821 \u2192 basis A013609","chain":null}