A090363 Shifts 1 place left under the BINOMIAL transform of the self-convolution of this sequence.

1, 1, 3, 12, 58, 320, 1954, 12961, 92237, 698111, 5583319, 46952892, 413560076, 3803165348, 36419879176, 362366133696, 3738804161990, 39935163833132, 440917642476858, 5025099681646374, 59044001774803872, 714419979588724854

Offset

0,3

Links

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

Formula

G.f.: A(x) = 1 + A(x/(1-x))^2*x/(1-x).

Prog

(PARI) {a(n)=local(A); if(n<0, 0, A=1+x+x*O(x^n); for(k=1, n, B=subst(A^2, x, x/(1-x))/(1-x)+x*O(x^n); A=1+x*B); polcoeff(A, n, x))}
(Maxima) a(n):=if n=0 then 1 else sum(binomial(n-1, k-1)*sum(a(k-1-i)*a(i), i, 0, k-1), k, 1, n); /* Vladimir Kruchinin, Jun 25 2011 */

Crossrefs

Sequence in context: A369594 A369403 A291488 * A115086 A258173 A196708

Adjacent sequences: A090360 A090361 A090362 * A090364 A090365 A090366

Keyword

nonn

Author

Paul D. Hanna, Nov 26 2003

Status

approved