A376582 Triangle of generalized Stirling numbers.

1, 5, 1, 26, 7, 1, 154, 47, 9, 1, 1044, 342, 74, 11, 1, 8028, 2754, 638, 107, 13, 1, 69264, 24552, 5944, 1066, 146, 15, 1, 663696, 241128, 60216, 11274, 1650, 191, 17, 1, 6999840, 2592720, 662640, 127860, 19524, 2414, 242, 19, 1, 80627040, 30334320, 7893840, 1557660, 245004, 31594, 3382, 299, 21, 1

Offset

0,2

Links

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

Formula

T(m,n,k) = Sum_{i=0..n-k} Stirling1(i+m,m)*binomial(n+m+1,n-k-i)*(n+m-k)!/(i+m)!, for m=1.

Example

Triangle starts:
[0]       1;
[1]       5,       1;
[2]      26,       7,       1;
[3]     154,      47,       9,        1;
[4]    1044,     342,      74,       11,       1;
[5]    8028,    2754,     638,      107,      13,     1;
[6]   69264,   24552,    5944,     1066,     146,    15,    1;
[7]  663696,  241128,   60216,    11274,    1650,   191,   17,    1;

Maple

T:=(m, n, k)->add(Stirling1(i+m, m)*binomial(n+m+1, n-k-i)*(n+m-k)!/(i+m)!, i=0..n-k): m:=1: seq(seq(T(m, n, k), k=0..n), n=0..10);

Crossrefs

Column k: A001705 (k=0), A001711 (k=1), A001716 (k=2), A001721 (k=3), A051524 (k=4), A051545 (k=5), A051560 (k=6).

Cf. A094587 and A173333 for m=0.

Sequence in context: A264131 A075500 A096645 * A140713 A125906 A146414

Adjacent sequences: A376579 A376580 A376581 * A376583 A376584 A376585

Keyword

nonn,tabl

Author

Igor Victorovich Statsenko, Sep 29 2024

Status

approved