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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

Table of n, a(n) for n=0..54.

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.)