A088715 G.f. satisfies: A(x*g(x)) = g(x) where g(x) is the g.f. of A088716.

1, 1, 2, 7, 36, 240, 1926, 17815, 184916, 2116498, 26391700, 355405934, 5134778584, 79178537346, 1297633495518, 22522717498167, 412754532495252, 7965288555078018, 161475849044919996, 3431346397643014818

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..440

Formula

G.f.: Coefficient of x^n in A(x)^(n+1)/(n+1) = coefficient of x^n in A(x)^(n+2) = A088716(n).

G.f. satisfies: A(x) = exp( Sum_{n>=1} x^n/(1 - x*[A'(x)/A(x)])^n/n ). - Paul D. Hanna, Aug 31 2009

G.f. satisfies: A(x) = 1 + x*A(x)^2/(A(x) - x*A'(x)). - Paul D. Hanna, Mar 20 2013

a(n) ~ c * n! * n^2, where c = A238223 / exp(1) = 0.08017961462469262235245081077906956577... - Vaclav Kotesovec, Feb 21 2014

Prog

(PARI) a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=exp(sum(k=1, n, (1-x*deriv(log(A)))^(-k)*x^k/k))); polcoeff(A, n) \\ Paul D. Hanna, Aug 31 2009
(PARI) a(n)=local(A=1+x); for(i=1, n, A=1+x*A^2/(A-x*deriv(A)+x*O(x^n))); polcoeff(A, n)
for(n=0, 30, print1(a(n), ", ")) \\ Paul D. Hanna, Mar 20 2013

Crossrefs

Cf. A088716, A238223.

Sequence in context: A119736 A353166 A308750 * A373773 A088313 A201197

Adjacent sequences: A088712 A088713 A088714 * A088716 A088717 A088718

Keyword

nonn

Author

Paul D. Hanna, Oct 12 2003

Status

approved