OFFSET
0,2
COMMENTS
Self-convolution of A000699 (after ignoring the initial term), [previous name].
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. A(x) = 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
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 04 2005
EXTENSIONS
Name replaced with an existing formula by Paul D. Hanna, Sep 16 2024
STATUS
approved