A182356 G.f. satisfies: A(x) = d/dx log(1+x + x^2*A(x)^2).

1, 1, 4, 29, 286, 3478, 49750, 813949, 14951218, 304272526, 6791813216, 164961150626, 4331176071496, 122252442659992, 3692061705866554, 118804126659832861, 4058311931802683890, 146684121878245070758, 5593222574333657589416, 224400536392956665317414

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..300

Formula

G.f. satisfies: A(x) = (1 + 2*x*A(x)^2 - x^2*A(x)^3) / (1+x - 2*x^2*A'(x)).

a(n) ~ c * n * 2^n * n!, where c = 0.1840416364326449945692... - Vaclav Kotesovec, Aug 24 2017

Example

G.f.: A(x) = 1 + x + 4*x^2 + 29*x^3 + 286*x^4 + 3478*x^5 + 49750*x^6 +...
such that
log(1+x + x^2*A(x)^2) = x + x^2/2 + 4*x^3/3 + 29*x^4/4 + 286*x^5/5 + 3478*x^6/6 + 49750*x^7/7 +...+ a(n-1)*x^n/n +...
Related expansions.
1+x + x^2*A(x)^2 = 1 + x + x^2 + 2*x^3 + 9*x^4 + 66*x^5 + 646*x^6 + 7760*x^7 109585*x^8 +...+ A259607(n)*x^n +...
A(x)^2 = 1 + 2*x + 9*x^2 + 66*x^3 + 646*x^4 + 7760*x^5 + 109585*x^6 +...+ A259607(n+2)*x^n +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=deriv(log(1+x + x^2*A^2 +x^2*O(x^n)))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A259607.

Sequence in context: A370955 A294160 A160885 * A083072 A302586 A302609

Adjacent sequences: A182353 A182354 A182355 * A182357 A182358 A182359

Keyword

nonn

Author

Paul D. Hanna, Apr 26 2012

Status

approved