A185183 G.f. A(x) satisfies: A(x) = 1+x + x^2*[d/dx A(x)^2].

1, 1, 2, 10, 72, 672, 7640, 102072, 1564864, 27064448, 521248320, 11064781760, 256702399360, 6462978471168, 175520877380992, 5115062135795584, 159227683153536000, 5273353734210310144, 185143079148664099840, 6869062513111759635456

Offset

0,3

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..400

Formula

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

a(n) ~ c * n! * 2^n / sqrt(n), where c = 0.493602095524198015213766719826126125048... - Vaclav Kotesovec, Feb 21 2014

a(0) = a(1) = 1; a(n) = (n-1) * Sum_{k=0..n-1} a(k) * a(n-k-1). - Ilya Gutkovskiy, Jul 05 2020

Example

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 72*x^4 + 672*x^5 + 7640*x^6 +...
Related series:
A(x)^2 = 1 + 2*x + 5*x^2 + 24*x^3 + 168*x^4 + 1528*x^5 + 17012*x^6 +...
d/dx A(x)^2 = 2 + 10*x + 72*x^2 + 672*x^3 + 7640*x^4 + 102072*x^5 +...

Prog

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

Crossrefs

Cf. A143916, A218223, A218224.

Sequence in context: A182525 A321389 A292406 * A052555 A204808 A084844

Adjacent sequences: A185180 A185181 A185182 * A185184 A185185 A185186

Keyword

nonn

Author

Paul D. Hanna, Mar 12 2012

Status

approved