A184730 G.f.: exp( Sum_{n>=1} A184731(n)*x^n/n ) where A184731(n) = Sum_{k=0..n} C(n,k)^(k+1).

1, 2, 5, 20, 159, 3152, 168036, 20428850, 5796209814, 4052041564524, 6210335115944263, 21470958882165989854, 183818137919395949397148, 3517964195874870876682733562, 147909303669340763210833833705995, 15391220509661795085065182391703575606

Offset

0,2

Comments

Note that the following g.f. does NOT yield an integer series:

. exp( Sum_{n>=1} [Sum_{k=0..n} C(n,k)^k] * x^n/n ).

Links

Seiichi Manyama, Table of n, a(n) for n = 0..74

Formula

Equals row sums of triangle A228899.

a(0) = 1, a(n) = (1/n)*Sum_{k=1..n} A184731(k)*a(n-k) for n > 0. - Seiichi Manyama, Jan 10 2019

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 20*x^3 + 159*x^4 + 3152*x^5 +...
log(A(x)) = 2*x + 6*x^2/2 + 38*x^3/3 + 490*x^4/4 + 14152*x^5/5 + 969444*x^6/6 +...+ A184731(n)*x^n/n +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^(k+1))*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A184731, A181070, A228899.

Sequence in context: A229662 A111885 A159320 * A181076 A156871 A058109

Adjacent sequences: A184727 A184728 A184729 * A184731 A184732 A184733

Keyword

nonn

Author

Paul D. Hanna, Jan 20 2011

Status

approved