A159597 G.f.: A(x) = exp( Sum_{n>=1} [ D^n x/(1-x)^3 ]^n/n ), where differential operator D = x*d/dx.

1, 1, 7, 37, 245, 2094, 24661, 410376, 9809637, 334520167, 16192227784, 1107914634442, 106788033119369, 14525652771018918, 2780328926392863928, 751651711717655433750, 286240041470280077141769

Offset

0,3

Links

Table of n, a(n) for n=0..16.

Formula

G.f.: A(x) = exp( Sum_{n>=1} [Sum_{k>=1} k^n*k(k+1)/2*x^k]^n/n ) where A(x) = Sum_{k>=1} a(k)*x^k.

Example

G.f.: A(x) = 1 + x + 7*x^2 + 37*x^3 + 245*x^4 + 2094*x^5 +...
log(A(x)) = Sum_{n>=1} [x + 2^n*3*x^2 + 3^n*6*x^3 +...]^n/n.
D^n x/(1-x)^3 = x + 2^n*3*x^2 + 3^n*6*x^3 + 4^n*10*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*k*(k+1)/2*x^k+x*O(x^n))^m/m))); polcoeff(A, n)}

Crossrefs

Cf. A156170, A159596, A159598.

Sequence in context: A332906 A361279 A096965 * A217723 A100309 A198410

Adjacent sequences: A159594 A159595 A159596 * A159598 A159599 A159600

Keyword

nonn

Author

Paul D. Hanna, May 05 2009

Status

approved