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
Links
- 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