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 A269952 Triangle read by rows, T(n,k) = Sum_{j=0..n} (-1)^(n-j)*C(-j,-n)*S2(j,k), S2 the Stirling set numbers A048993, for n>=0 and 0<=k<=n. 2
 1, 0, 1, 0, 2, 1, 0, 4, 5, 1, 0, 8, 19, 9, 1, 0, 16, 65, 55, 14, 1, 0, 32, 211, 285, 125, 20, 1, 0, 64, 665, 1351, 910, 245, 27, 1, 0, 128, 2059, 6069, 5901, 2380, 434, 35, 1, 0, 256, 6305, 26335, 35574, 20181, 5418, 714, 44, 1 (list; table; graph; refs; listen; history; text; internal format)
 OFFSET 0,5 LINKS Peter Luschny, Extensions of the binomial FORMULA T(n, k) = S2(n+1, k+1) - S2(n, k+1). EXAMPLE 1, 0, 1, 0, 2, 1, 0, 4, 5, 1, 0, 8, 19, 9, 1, 0, 16, 65, 55, 14, 1, 0, 32, 211, 285, 125, 20, 1, 0, 64, 665, 1351, 910, 245, 27, 1. MAPLE A269952 := (n, k) -> Stirling2(n+1, k+1) - Stirling2(n, k+1): seq(seq(A269952(n, k), k=0..n), n=0..9); MATHEMATICA Flatten[ Table[ Sum[(-1)^(n-j) Binomial[-j, -n] StirlingS2[j, k], {j, 0, n}], {n, 0, 9}, {k, 0, n}]] CROSSREFS Variant: A143494 (the main entry for this triangle). A005493 (row sums), A074051 (alt. row sums), A000079 (col. 1), A001047 (col. 2), A016269 (col. 3), A025211 (col. 4), A000096 (diag. n,n-1), A215862 (diag. n,n-2), A049444, A136124, A143491 (matrix inverse). Cf. A048993, A269951. Sequence in context: A100887 A073592 A164994 * A247268 A266867 A151852 Adjacent sequences:  A269949 A269950 A269951 * A269953 A269954 A269955 KEYWORD nonn,tabl AUTHOR Peter Luschny, Apr 10 2016 STATUS approved

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Last modified January 17 16:01 EST 2021. Contains 340245 sequences. (Running on oeis4.)