A089278 Coefficient triangle for computation of column numbers of triangle A071951 (Legendre-Stirling).

1, -1, 3, 1, -15, 24, -7, 405, -2268, 2500, 2, -405, 6048, -20000, 16875, -11, 7425, -266112, 2000000, -4640625, 3176523, 143, -312741, 25474176, -390000000, 1879453125, -3344878719, 1927561216, -143, 995085, -178319232, 5250000000, -46986328125, 163899057231, -236126248960

Offset

1,3

Comments

The k-th column sequence A071951(n+k,k), n>=0, is sum(a(k,p)*(p*(p+1))^n,p=1..k)/A089500(k), k>=1.

Links

Table of n, a(n) for n=1..35.

W. Lang, First 7 rows.

Formula

a(n, m)= A089500(n)*(((-1)^(m+n))*(2*m+1)*((m*(m+1))^n)/((m+n+1)!*(n-m)!)).

Example

[1]; [ -1,3]; [1,-15,24]; [ -7,405,-2268,2500]; ...
Sequence A071951(n+3,3)= A016309(n)= [1,20,292,...] has a(n)=
(1*(1*2)^n - 15*(2*3)^n + 24*(3*4)^n)/10.

Crossrefs

Sequence in context: A284861 A284234 A365338 * A213245 A053485 A160628

Adjacent sequences: A089275 A089276 A089277 * A089279 A089280 A089281

Keyword

sign,tabl

Author

Wolfdieter Lang, Nov 07 2003

Status

approved