A137973 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^5.

1, 1, 5, 40, 355, 3495, 36251, 391650, 4355810, 49550130, 573811635, 6742112506, 80175836395, 963137138105, 11670425726255, 142471372540290, 1750641388279500, 21634966222174020, 268734270298502640

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

G.f.: A(x) = 1 + x*B(x)^5 where B(x) is the g.f. of A137974.

a(n) = Sum_{k=0..n-1} C(5*(n-k),k)/(n-k) * C(6*k,n-k-1) for n>0 with a(0)=1. - Paul D. Hanna, Jun 16 2009

a(n) ~ sqrt(5*s*(1-s)*(6-7*s) / ((348*s - 300)*Pi)) / (n^(3/2) * r^n), where r = 0.0739607593319208338998816978154858830062403258604... and s = 1.212436147090690045831533523759068212147683922018... are real roots of the system of equations s = 1 + r*(1 + r*s^6)^5, 30 * r^2 * s^5 * (1 + r*s^6)^4 = 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^6)^5); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(5*(n-k), k)/(n-k)*binomial(6*k, n-k-1))) \\ Paul D. Hanna, Jun 16 2009

Crossrefs

Cf. A137974, A137972; A137961, A137963, A137965.

Sequence in context: A007036 A264227 A052798 * A371520 A052788 A213104

Adjacent sequences: A137970 A137971 A137972 * A137974 A137975 A137976

Keyword

nonn

Author

Paul D. Hanna, Feb 26 2008

Status

approved