OFFSET
0,3
FORMULA
a(n)=Sum(C(n, k)Sum(i!i Stirling2(k, i), i=1, .., k)Sum(i!i Stirling2(n-k, i), i=1, .., n-k), k=0, .., n)
E.g.f.: (exp(x)-1)^2 / (2-exp(x))^4. - Vaclav Kotesovec, May 07 2019
a(n) ~ n! * n^3 / (96 * log(2)^(n+4)). - Vaclav Kotesovec, May 07 2019
MATHEMATICA
Table[ Sum[Binomial[n, k]Sum[i!i StirlingS2[k, i], {i, 1, k}]Sum[i!i StirlingS2[n - k, i], {i, 1, n - k}], {k, 0, n}], {n, 0, 20}]
nmax = 20; CoefficientList[Series[(E^x-1)^2 / (2-E^x)^4, {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, May 07 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Mario Catalani (mario.catalani(AT)unito.it), Jan 01 2004
STATUS
approved