A216585 G.f.: exp( Sum_{n>=1} A000984(n)*A002426(n)*x^n/n ), where A000984 is the central binomial coefficients and A002426 is the central trinomial coefficients.

1, 2, 11, 66, 485, 3842, 32712, 291568, 2697610, 25679316, 250190125, 2484270622, 25062816127, 256275246582, 2650947762450, 27697861115740, 291943603838698, 3101066786857876, 33167191013319532, 356924515784037128, 3862299973917286526, 42003704374124712172

Offset

0,2

Links

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

Formula

Logarithmic derivative yields A216584.

Example

G.f.: A(x) = 1 + 2*x + 11*x^2 + 66*x^3 + 485*x^4 + 3842*x^5 + 32712*x^6 +...
such that
log(A(x)) = 2*1*x + 6*3*x^2/2 + 20*7*x^3/3 + 70*19*x^4/4 + 252*51*x^5/5 + 924*141*x^6/6 +...+ A000984(n)*A002426(n)*x^n/n +...

Prog

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

Crossrefs

Cf. A216584, A216586, A002426, A000984.

Sequence in context: A391461 A160852 A185627 * A245277 A138792 A058056

Adjacent sequences: A216582 A216583 A216584 * A216586 A216587 A216588

Keyword

nonn

Author

Paul D. Hanna, Sep 09 2012

Status

approved