A216586 G.f.: exp( Sum_{n>=1} A002426(n)/2 * A002426(n) * x^n/n ), where A002426 is the central binomial coefficients and A002426 is the central trinomial coefficients.

1, 1, 5, 28, 202, 1579, 13375, 118858, 1098458, 10453452, 101872926, 1012109860, 10218226307, 104570617520, 1082633236498, 11321654913838, 119438468577559, 1269787015989428, 13592294300856138, 146390465351654178, 1585337895099162317, 17253991887494062080

Offset

0,3

Links

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

Formula

Self-convolution yields A216585.

Example

G.f.: A(x) = 1 + x + 5*x^2 + 28*x^3 + 202*x^4 + 1579*x^5 + 13375*x^6 +...
such that
log(A(x)) = 1*1*x + 3*3*x^2/2 + 10*7*x^3/3 + 35*19*x^4/4 + 126*51*x^5/5 + 462*141*x^6/6 +...+ A001700(n)*A002426(n)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, binomial(2*m, m)/2*polcoeff((1+x+x^2)^m, m)*x^m/m+x*O(x^n))), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A216585, A002426, A001700, A000984.

Sequence in context: A318364 A064898 A368792 * A151500 A356409 A332711

Adjacent sequences: A216583 A216584 A216585 * A216587 A216588 A216589

Keyword

nonn

Author

Paul D. Hanna, Sep 09 2012

Status

approved