A253255 G.f. satisfies: A(x) = (1 - x^3*A(x)^3)^2 / (1 - x*A(x))^4.

1, 4, 26, 202, 1731, 15780, 150117, 1473292, 14807363, 151638550, 1576616125, 16598802248, 176599380271, 1895767748376, 20508188211018, 223348309510194, 2446792909432683, 26944972018189698, 298111489130625351, 3312016395569631402, 36935315970911333184, 413308467174788509668

Offset

0,2

Comments

Self-convolution of A253256.

Links

Table of n, a(n) for n=0..21.

Formula

G.f. A(x) satisfies:

(1) A(x) = exp( Sum_{n>=1} A168595(n)*x^n/n ), where A168595(n) = Sum_{k=0..2*n} binomial(n,k)*trinomial(n,k).

(2) A(x) = (1/x)*Series_Reversion( x*(1-x)^4/(1-x^3)^2 ).

Example

G.f.: A(x) = 1 + 4*x + 26*x^2 + 202*x^3 + 1731*x^4 + 15780*x^5 +...
where A(x) = (1 - x^3*A(x)^3)^2 / (1 - x*A(x))^4.
The logarithm begins:
log(A(x)) = 4*x + 36*x^2/2 + 358*x^3/3 + 3748*x^4/4 + 40404*x^5/5 + 443886*x^6/6 + 4941654*x^7/7 +...+ A168595(n)*x^n/n +...

Prog

(PARI) {a(n) = local(A=1); A = (1/x)*serreverse( x*(1-x)^4/(1-x^3)^2 +x^2*O(x^n)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))
(PARI) {A168595(n) = sum(k=0, 2*n, binomial(2*n, k) * polcoeff((1+x+x^2)^n, k) )}
{a(n) = local(A=1); A = exp( sum(k=1, n+1, A168595(k)*x^k/k) +x*O(x^n)); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A168595, A106228, A064641, A253256.

Sequence in context: A246509 A369107 A368976 * A141381 A369124 A118971

Adjacent sequences: A253252 A253253 A253254 * A253256 A253257 A253258

Keyword

nonn

Author

Paul D. Hanna, May 31 2015

Status

approved