A137967 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^2.

1, 1, 2, 13, 66, 406, 2602, 17271, 118444, 829514, 5914980, 42791085, 313277294, 2316793170, 17281455882, 129867946828, 982293317064, 7472406051744, 57132051350160, 438797394096378, 3383870656327576, 26191385476141936

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

G.f.: A(x) = 1 + x*B(x)^2 where B(x) is the g.f. of A137968.

a(n) = Sum_{k=0..n-1} C(2*(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(2*s*(1-s)*(6-7*s) / ((132*s - 120)*Pi)) / (n^(3/2) * r^n), where r = 0.1201742080825038015263858974579392344239858277873... and s = 1.297009871974239150024579315539982910111693413337... are real roots of the system of equations s = 1 + r*(1 + r*s^6)^2, 12 * r^2 * s^5 * (1 + r*s^6) = 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)^2); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(2*(n-k), k)/(n-k)*binomial(6*k, n-k-1))) \\ Paul D. Hanna, Jun 16 2009

Crossrefs

Cf. A137968, A137966; A137952, A137955, A137960.

Sequence in context: A160459 A037752 A037640 * A045764 A106999 A054566

Adjacent sequences: A137964 A137965 A137966 * A137968 A137969 A137970

Keyword

nonn

Author

Paul D. Hanna, Feb 26 2008

Status

approved