A113662 G.f. satisfies: A(x) = (1 + x*(d/dx x*A(x)) )^2.

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

Offset: 0

Author

Paul D. Hanna, Nov 04 2005

Keywords

• nonn

Comments

Self-convolution of A000699 (after ignoring the initial term), [previous name].

Examples

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

Links

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

Crossrefs

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

Programs

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

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

Extensions

Name replaced with an existing formula by Paul D. Hanna, Sep 16 2024