%I #29 May 06 2022 13:31:41

%S 1,0,2,-6,34,-220,1688,-14868,147684,-1631376,19821912,-262573080,

%T 3764276712,-58044604176,957653604672,-16828739439120,313742795670288,

%U -6183918938706048,128463999017594016,-2804979941504113248

%N Expansion of e.g.f. exp(log(1+x)^2).

%H Seiichi Manyama, <a href="/A009199/b009199.txt">Table of n, a(n) for n = 0..446</a>

%H INRIA Algorithms Project, <a href="http://ecs.inria.fr/services/structure?nbr=128">Encyclopedia of Combinatorial Structures 128</a>

%F a(n) = Sum_{k=0..floor(n/2)} Stirling1(n, 2*k)*(2*k)!/k!. - _Vladeta Jovovic_, Sep 21 2003

%F E.g.f.: (1+x)^(log(1+x)). - _Vaclav Kotesovec_, Jul 31 2018

%F 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

%t CoefficientList[Series[E^(Log[1+x]^2), {x, 0, 20}], x] * Range[0, 20]! (* _Vaclav Kotesovec_, Jul 02 2015 *)

%o (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

%K sign,easy

%O 0,3

%A _R. H. Hardin_

%E Extended with signs by _Olivier Gérard_, Mar 15 1997