A351505 Expansion of e.g.f. 1/(1 + x^2/2 * log(1 - x)).
1, 0, 0, 3, 6, 20, 270, 1764, 12600, 146880, 1597680, 17934840, 243777600, 3506518080, 52696595952, 870564618000, 15354480960000, 284780747946240, 5622461683666560, 117425971162442880, 2574172644658272000, 59302473667128599040, 1432738540209781728000
Offset: 0
Keywords
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..443
Programs
-
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1+x^2/2*log(1-x)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=i!/2*sum(j=3, i, 1/(j-2)*v[i-j+1]/(i-j)!)); v;
-
PARI
a(n) = n!*sum(k=0, n\3, k!*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
Formula
a(0) = 1; a(n) = n!/2 * Sum_{k=3..n} 1/(k-2) * a(n-k)/(n-k)!.
a(n) = n! * Sum_{k=0..floor(n/3)} k! * |Stirling1(n-2*k,k)|/(2^k * (n-2*k)!).