A238300 Fourth convolution of A107841.
1, 8, 64, 520, 4304, 36232, 309504, 2677128, 23405520, 206522888, 1836913216, 16452907016, 148274884688, 1343569891720, 12233903203328, 111883174439304, 1027244073375312, 9465236716896264, 87498251217286720, 811252609543727624, 7542152541765899728, 70294794046928531848
Offset: 0
Links
- Fung Lam, Table of n, a(n) for n = 0..1000
Programs
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Mathematica
CoefficientList[Series[((1+x-Sqrt[1-10*x+x^2])/(6*x))^4,{x,0,20}],x] (* Vaclav Kotesovec, Feb 27 2014 *)
Formula
G.f.: (G.f. of A107841)^4.
Recurrence: (n+4)*a(n) = (8-n)*a(n-8) + 4*(4*n-26)*a(n-7) + 64*(5-n)*a(n-6) + 8*(2*n-7)*a(n-5) + 194*(n-2)*a(n-4) + 8*(2*n-1)*a(n-3) - 64*(n+1)*a(n-2) + 8*(2*n+5)*a(n-1), n>=8.
Recurrence (of order 2): n*(n+4)*(2*n+1)*a(n) = 20*n*(n+1)*(n+2)*a(n-1) - (n-2)*(n+2)*(2*n+3)*a(n-2). - Vaclav Kotesovec, Feb 27 2014
a(n) ~ 2*sqrt(35280+14403*sqrt(6)) * (5+2*sqrt(6))^n / (27 * sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 27 2014