A159596 G.f.: A(x) = exp( Sum_{n>=1} [ D^n x/(1-x)^2 ]^n/n ), where differential operator D = x*d/dx.

1, 1, 5, 22, 121, 863, 8476, 118131, 2361313, 67467236, 2731757961, 156417295405, 12605225573076, 1432381581679361, 229016092616239411, 51628631138952017332, 16402709158903948390585, 7351149638643155728435357

Offset

0,3

Comments

Conjecture: limit_{n->oo} a(n)^(1/n^2) = 2^(1/4). - Vaclav Kotesovec, Nov 17 2023

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..113

Formula

G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^(n+1)*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.

Example

G.f.: A(x) = 1 + x + 5*x^2 + 22*x^3 + 121*x^4 + 863*x^5 +...
log(A(x)) = Sum_{n>=1} [x + 2^(n+1)*x^2 + 3^(n+1)*x^3 +...]^n/n.
D^n x/(1-x)^2 = x + 2^(n+1)*x^2 + 3^(n+1)*x^3 + 4^(n+1)*x^4 +...

Prog

(PARI) {a(n)=local(A=1+x); for(i=1, n, A=exp(sum(m=1, n, sum(k=1, n, k^(m+1)*x^k+x*O(x^n))^m/m))); polcoeff(A, n)}

Crossrefs

Cf. A156170, A159597, A159598.

Sequence in context: A326341 A062794 A036235 * A020077 A265998 A203265

Adjacent sequences: A159593 A159594 A159595 * A159597 A159598 A159599

Keyword

nonn

Author

Paul D. Hanna, May 05 2009

Status

approved