A089277 Sixth column of the triangle A071951 (Legendre-Stirling).

1, 112, 7896, 453056, 23232176, 1113673728, 51155215360, 2284897159168, 100157064553728, 4334351404617728, 185915811851773952, 7925465707325177856, 336395829865869340672, 14234737653310804590592

Offset

0,2

Links

Table of n, a(n) for n=0..13.

Index entries for linear recurrences with constant coefficients, signature (112,-4648,89280,-808848,3110400,-3628800).

Formula

G.f.: 1/Product_{p=1..6} (1 - p*(p+1)*x) = 1/((1-2*x)*(1-6*x)*(1-12*x)*(1-20*x)*(1-30*x)*(1-42*x)).

a(n) = A071951(n+6, 6), n>=0.

a(n) = (Sum_{p=1..6} A089278(6, p)*(p*(p+1))^n)/A089500(6) = (-11*2^n + 7425*6^n - 266112*12^n + 2000000*20^n - 4640625*30^n + 3176523*42^n)/277200.

a(n) = det(|ps(i+6,j+5)|, 1 <= i,j <= n), where ps(n,k) are Legendre-Stirling numbers of the first kind (A129467). - Mircea Merca, Apr 06 2013

Crossrefs

Cf. A071951, A071952, A089274, A089278, A089500, A129467.

Sequence in context: A035813 A223613 A075910 * A203788 A180027 A240229

Adjacent sequences: A089274 A089275 A089276 * A089278 A089279 A089280

Keyword

nonn,easy

Author

Wolfdieter Lang, Nov 07 2003

Status

approved