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
Keywords
Examples
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 +...
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..74
Programs
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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)}
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
Comments