A137964 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^5)^4.

1, 1, 4, 26, 184, 1451, 12020, 103734, 921132, 8364877, 77317704, 725029730, 6880482816, 65955731874, 637703938860, 6211709281162, 60900108419200, 600486291654444, 5950951929703520, 59242473406384472, 592166933647780576

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..350

Formula

G.f.: A(x) = 1 + x*B(x)^4 where B(x) is the g.f. of A137965.

a(n) = Sum_{k=0..n-1} C(4*(n-k),k)/(n-k) * C(5*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009

a(n) ~ sqrt(4*s*(1-s)*(5-6*s) / ((190*s - 160)*Pi)) / (n^(3/2) * r^n), where r = 0.0927175295193852172913829423030505161354091369581... and s = 1.270497495855793662015513509713357933752729700697... are real roots of the system of equations s = 1 + r*(1 + r*s^5)^4, 20 * r^2 * s^4 * (1 + r*s^5)^3 = 1. - Vaclav Kotesovec, Nov 22 2017

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=0, n, A=1+x*(1+x*A^5)^4); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(4*(n-k), k)/(n-k)*binomial(5*k, n-k-1))) \\ Paul D. Hanna, Jun 16 2009

Crossrefs

Cf. A137965, A137963; A137956, A137958, A137971.

Sequence in context: A098443 A264226 A052775 * A107649 A371517 A052763

Adjacent sequences: A137961 A137962 A137963 * A137965 A137966 A137967

Keyword

nonn

Author

Paul D. Hanna, Feb 26 2008

Status

approved