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 A168621 Triangle read by rows: T(n,0) = T(n,n) = 1 for n >= 0, T(n,k) = ((n - 1)! + 1)*binomial(n, k) for 1 <= k <= n - 1, n >= 2. 0
 1, 1, 1, 1, 4, 1, 1, 9, 9, 1, 1, 28, 42, 28, 1, 1, 125, 250, 250, 125, 1, 1, 726, 1815, 2420, 1815, 726, 1, 1, 5047, 15141, 25235, 25235, 15141, 5047, 1, 1, 40328, 141148, 282296, 352870, 282296, 141148, 40328, 1, 1, 362889, 1451556, 3386964, 5080446, 5080446, 3386964, 1451556, 362889, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 COMMENTS Row 0 is 1, and row n gives the coefficients in the expansion of (x + 1)^n + (n - 1)!*((x + 1)^n - x^n -1). - Franck Maminirina Ramaharo, Dec 22 2018 LINKS FORMULA From Franck Maminirina Ramaharo, Dec 22 2018: (Start) T(n,k) = A007318(n,k) + A219570(n,k) for 1 <= k <= n - 1, n >= 2. E.g.f.: exp((1 + x)*y) + log((1 - y)*(1 - x*y)/(1 - (1 + x)*y)). (End) EXAMPLE Triangle begins:   1;   1,     1;   1,     4,      1;   1,     9,      9,      1;   1,    28,     42,     28,      1;   1,   125,    250,    250,    125,      1;   1,   726,   1815,   2420,   1815,    726,      1;   1,  5047,  15141,  25235,  25235,  15141,   5047,     1;   1, 40328, 141148, 282296, 352870, 282296, 141148, 40328, 1;   ... MATHEMATICA p[x_, n_] := If[n == 0, 1, (x + 1)^n + (n - 1)!*((x + 1)^n - x^n - 1)]; Table[CoefficientList[p[x, n], x], {n, 0, 12}] // Flatten (* Franck Maminirina Ramaharo, Dec 22 2018 *) PROG (Maxima) T(n, k) := if k = 0 or k = n then 1 else ((n - 1)! + 1)*binomial(n, k)\$ create_list(T(n, k), n, 0, 12, k, 0, n); /* Franck Maminirina Ramaharo, Dec 22 2018 */ CROSSREFS Row sums: A154252. Cf. A007318, A132047, A155863, A155864, A155865 A168619, A219570. Sequence in context: A155451 A220681 A189280 * A039756 A126065 A299427 Adjacent sequences:  A168618 A168619 A168620 * A168622 A168623 A168624 KEYWORD nonn,tabl,easy AUTHOR Roger L. Bagula and Gary W. Adamson, Dec 01 2009 EXTENSIONS Edited by Franck Maminirina Ramaharo, Dec 22 2018 (previous definition and examples were the same as A168620, but with different entries, as pointed out by R. J. Mathar, Oct 21 2012) STATUS approved

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Last modified May 14 10:11 EDT 2021. Contains 343880 sequences. (Running on oeis4.)