OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..446
INRIA Algorithms Project, Encyclopedia of Combinatorial Structures 128
FORMULA
a(n) = Sum_{k=0..floor(n/2)} Stirling1(n, 2*k)*(2*k)!/k!. - Vladeta Jovovic, Sep 21 2003
E.g.f.: (1+x)^(log(1+x)). - Vaclav Kotesovec, Jul 31 2018
a(0) = 1; a(n) = 2 * Sum_{k=1..n} binomial(n-1,k-1) * Stirling1(k,2) * a(n-k). - Seiichi Manyama, May 06 2022
MATHEMATICA
CoefficientList[Series[E^(Log[1+x]^2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 02 2015 *)
PROG
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, binomial(i-1, j-1)*stirling(j, 2, 1)*v[i-j+1])); v; \\ Seiichi Manyama, May 06 2022
CROSSREFS
KEYWORD
sign,easy
AUTHOR
EXTENSIONS
Extended with signs by Olivier Gérard, Mar 15 1997
STATUS
approved