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A216358 G.f.: 1/( (1-32*x)*(1+11*x-x^2)^2 )^(1/5). 2
1, 2, 129, 2258, 66266, 1711282, 48405689, 1366932878, 39516211006, 1152710434262, 33978897474149, 1008971023405798, 30155867955237721, 906105094582017192, 27351768342997448884, 828919276503075367768, 25208280600556937464286, 768948732346237772809572 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..17.

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

EXAMPLE

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 +...

PROG

(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), ", "))

CROSSREFS

Cf. A216316, A216357, A070782.

Sequence in context: A003369 A303377 A258806 * A294274 A099824 A300292

Adjacent sequences:  A216355 A216356 A216357 * A216359 A216360 A216361

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Sep 04 2012

STATUS

approved

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Last modified April 5 21:46 EDT 2020. Contains 333260 sequences. (Running on oeis4.)