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

0,2

Links

Fung Lam, Table of n, a(n) for n = 0..1000

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

Mathematica

CoefficientList[Series[((1+x-Sqrt[1-10*x+x^2])/(6*x))^4, {x, 0, 20}], x] (* Vaclav Kotesovec, Feb 27 2014 *)

Crossrefs

Cf. A107841, A238299.

Sequence in context: A074116 A245852 A033144 * A344271 A144317 A344054

Adjacent sequences: A238297 A238298 A238299 * A238301 A238302 A238303

Keyword

nonn,easy

Author

Fung Lam, Feb 25 2014

Status

approved