A137971 G.f. satisfies A(x) = 1 + x*(1 + x*A(x)^6)^4.

1, 1, 4, 30, 232, 2037, 18720, 179454, 1770380, 17864490, 183510672, 1912621814, 20175123732, 214980182783, 2310645275932, 25021270486830, 272717638241172, 2989549949264304, 32938634975109864, 364566094737276708

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 A137972.

a(n) = Sum_{k=0..n-1} C(4*(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(4*s*(1-s)*(6-7*s) / ((276*s - 240)*Pi)) / (n^(3/2) * r^n), where r = 0.0833821738312503523008482260558417829257343369560... and s = 1.229254439060935443156800948762443928645579909446... are real roots of the system of equations s = 1 + r*(1 + r*s^6)^4, 24 * r^2 * s^5 * (1 + r*s^6)^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^6)^4); polcoeff(A, n)}
(PARI) a(n)=if(n==0, 1, sum(k=0, n-1, binomial(4*(n-k), k)/(n-k)*binomial(6*k, n-k-1))) \\ Paul D. Hanna, Jun 16 2009

Crossrefs

Cf. A137972, A137970; A137956, A137958, A137964.

Sequence in context: A082144 A349456 A220727 * A346579 A300159 A213102

Adjacent sequences: A137968 A137969 A137970 * A137972 A137973 A137974

Keyword

nonn

Author

Paul D. Hanna, Feb 26 2008

Status

approved