A212426 a(n) = A212425(n) / (2*n-1).

1, 1, 6, 58, 704, 9765, 147870, 2382666, 40211406, 703391832, 12660466838, 233250098568, 4381343112174, 83656137696686, 1619826435181890, 31746893434751700, 628829271360548586, 12572386589515935168, 253455923387917072890

Offset

1,3

Links

Table of n, a(n) for n=1..19.

Formula

Given g.f. A(x), then G(x) = d/dx A(x^8)/(4*x^4) = Sum_{n>=1} (2*n-1)*a(n)*x^(8*n-5) is the g.f. of A212425 and satisfies: G(x) = (x + G(G(x)))^3.

Example

 G.f.: A(x) = x + x^2 + 6*x^3 + 58*x^4 + 704*x^5 + 9765*x^6 + 147870*x^7 +...
Let G(x) = d/dx A(x^8)/(4*x^4), then G(x) = (x + G(G(x)))^3, where
G(x) = x^3 + 3*x^11 + 30*x^19 + 406*x^27 + 6336*x^35 + 107415*x^43 +...
G(G(x)) = x^9 + 9*x^17 + 117*x^25 + 1788*x^33 + 29925*x^41 + 530910*x^49 +...

Prog

 (PARI) {a(n)=local(G=x^3+3*x^11); for(i=1, n, G=(x+subst(G, x, G +O(x^(8*n))))^3); polcoeff(G, 8*n-5)/(2*n-1)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A212425, A212391.

Sequence in context: A354228 A073848 A141382 * A259612 A305599 A316653

Adjacent sequences: A212423 A212424 A212425 * A212427 A212428 A212429

Keyword

nonn

Author

Paul D. Hanna, May 16 2012

Status

approved