A113662 Self-convolution of A000699.

1, 2, 9, 62, 566, 6372, 84837, 1300214, 22511322, 434226300, 9231983850, 214481625516, 5406323440492, 146963638311880, 4286068830850797, 133501081493969574, 4423404073559930162, 155359770700317171084

Offset

0,2

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

G.f. satisfies: A(x) = (1 + x*d/dx[x*A(x)] )^2.

a(n) ~ 2^(n + 5/2) * n^(n+1) / exp(n+1). - Vaclav Kotesovec, Oct 23 2020

Example

G.f. = 1 + 2*x + 9*x^2 + 62*x^3 + 566*x^4 + 6372*x^5 + 84837*x^6 + 1300214*x^7 + ...

Prog

(PARI) {a(n)=local(A=1+x*O(x^n)); for(i=1, n, A=(1+x*deriv(x*A))^2); polcoeff(A, n, x)}
(PARI)
A000699_seq(N) = {
  my(a = vector(N)); a[1] = 1;
  for (n=2, N, a[n] = sum(k=1, n-1, (2*k-1)*a[k]*a[n-k])); a;
};
Vec(sqr(Ser(A000699_seq(N))))  \\ Gheorghe Coserea, Jan 23 2017

Crossrefs

Cf. A000699, A113663, A113664, A113665, A113666, A113667, A113668.

Sequence in context: A268450 A146887 A173498 * A352326 A052820 A213528

Adjacent sequences: A113659 A113660 A113661 * A113663 A113664 A113665

Keyword

nonn

Author

Paul D. Hanna, Nov 04 2005

Status

approved