A383840 Expansion of 1/((1-x) * (1-4*x) * (1-9*x) * (1-16*x) * (1-25*x)).
1, 55, 2002, 61490, 1733303, 46587905, 1217854704, 31306548900, 796513723005, 20135227330075, 506945890951006, 12730754139133030, 319183135225967507, 7994212035818175365, 200089485703376577308, 5005984516439566690680, 125209574645032904521209
Offset: 0
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..714
- Index entries for linear recurrences with constant coefficients, signature (55,-1023,7645,-21076,14400).
Programs
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PARI
a(n) = (5*25^(n+4)-2*16^(n+5)+9^(n+6)-6*4^(n+6)+42)/362880;
Formula
a(n) = A269945(n+5,5).
a(n) = 55*a(n-1) - 1023*a(n-2) + 7645*a(n-3) - 21076*a(n-4) + 14400*a(n-5).
a(n) = (5*25^(n+4) - 2*16^(n+5) + 9^(n+6) - 6*4^(n+6) + 42)/362880.
sinh(x)^10/10! = Sum_{k>=0} 4^k * a(k) * x^(2*k+10)/(2*k+10)!.
a(n) = (1/10!) * Sum_{k=0..10} (-1)^k * (5-k)^(2*n+10) * binomial(10,k).
a(n) = Sum_{k=0..2*n} (-5)^k * binomial(2*n+10,k) * Stirling2(2*n-k+10,10).
a(n) = Sum_{k=0..2*n} (-1)^k * Stirling2(k+5,5) * Stirling2(2*n-k+5,5).