A216358 G.f.: 1/( (1-32*x)*(1+11*x-x^2)^2 )^(1/5).

1, 2, 129, 2258, 66266, 1711282, 48405689, 1366932878, 39516211006, 1152710434262, 33978897474149, 1008971023405798, 30155867955237721, 906105094582017192, 27351768342997448884, 828919276503075367768, 25208280600556937464286, 768948732346237772809572

Offset: 0

Author

Paul D. Hanna, Sep 04 2012

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + 2*x + 129*x^2 + 2258*x^3 + 66266*x^4 + 1711282*x^5 +...
where 1/A(x)^5 = 1 - 10*x - 585*x^2 - 3830*x^3 + 705*x^4 - 32*x^5.
The logarithm of the g.f. begins:
log(A(x)) = 2*x + 254*x^2/2 + 6008*x^3/3 + 215766*x^4/4 + 6643782*x^5/5 + 215492564*x^6/6 +...+ A070782(n)*x^n/n +...
		

Crossrefs

Cf. A216316, A216357, A070782.

Programs

PARI

{a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(j=0, m, binomial(5*m, 5*j))*x^m/m+x*O(x^n)))); polcoeff(A, n)}
for(n=0, 31, print1(a(n), ", "))

Formula

G.f.: exp( Sum_{n>=1} A070782(n)*x^n/n ) where A070782(n) = Sum_{k=0..n} binomial(5*n,5*k).

a(n) ~ 2^(5*n+3) * ((25-11*sqrt(5))/2)^(1/10) * GAMMA(4/5) / (5 * 11^(2/5) * n^(4/5) * Pi). - Vaclav Kotesovec, Jul 31 2014