A088223 Coefficient of x^n in g.f.^n is A048286(n).

1, 2, 3, 12, 93, 1032, 14655, 251688, 5052909, 115925904, 2990175786, 85643490420, 2697023236056, 92629652495280, 3446174110482327, 138077674608686544, 5928227839749416895, 271538262681756156768

Offset

0,2

Comments

Self-convolution of A240996.

Limit n->infinity A088223(n) / A240996(n) = 2. - Vaclav Kotesovec, Feb 11 2015

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..250

Formula

G.f. satisfies: (A(x)-x)^2 = A(x*A(x)). - Paul D. Hanna, Oct 15 2003

a(n) ~ c * 2^(n+1) * n^(n - 1/2 - log(2)/4) / (exp(n) * (log(2))^n), where c = 0.411579248322849751402... (see A240996). - Vaclav Kotesovec, Feb 11 2015

Prog

(PARI) {a(n)=local(A, m); if(n<1, n==0, m=1; A=1+x; for(i=1, n, A=subst(A, x, x*A+x*O(x^n))/(A-x) + x); polcoeff(A, n))}
for(n=0, 20, print1(a(n), ", ")) \\ Vaclav Kotesovec, Feb 11 2015

Crossrefs

Cf. A240996.

Sequence in context: A009594 A074179 A012586 * A162053 A162075 A333166

Adjacent sequences: A088220 A088221 A088222 * A088224 A088225 A088226

Keyword

nonn

Author

Michael Somos, Sep 24 2003

Status

approved