A182264 G.f. satisfies: A(x) = 1 + Sum_{n>=1} x^n/n! * d^n/dx^n x*A(x)^n.

1, 1, 4, 54, 1928, 164650, 32676492, 14876772190, 15354661251344, 35516102976906066, 182198338264587667220, 2054287821808180963790214, 50510836264662863485736461464, 2690257723573942460914976734069882, 308577942946685093647137438456317429148

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..77

Formula

a(n) ~ c * n! * 2^(n*(n-1)/2), where c = 1.429815286617205023097354008... - Vaclav Kotesovec, Feb 22 2014

Example

G.f.: A(x) = 1 + x + 4*x^2 + 54*x^3 + 1928*x^4 + 164650*x^5 + 32676492*x^6 +...

Prog

(PARI) {Dx(n, F)=local(D=F); for(i=1, n, D=deriv(D)); D} /* n-th derivative of F */
{a(n)=local(A=1+x+x*O(x^n)); for(i=1, n, A=1+sum(k=1, n, x^k/k!*Dx(k, x*A^k+x*O(x^n) ))); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))

Crossrefs

Cf. A182263.

Sequence in context: A265004 A284747 A003955 * A355128 A355126 A357511

Adjacent sequences: A182261 A182262 A182263 * A182265 A182266 A182267

Keyword

nonn

Author

Paul D. Hanna, Apr 21 2012

Status

approved