OFFSET
1,2
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 1..400
M. Maia and M. Mendez, On the arithmetic product of combinatorial species
FORMULA
a(n) = (1/(n-1)!)*Sum_{k=1..n} Stirling1(n,k)*b(k)^2, where b(n) = Sum_{k=1..n} (k-1)!*Stirling2(n,k).
a(n) ~ c * (n-1)! / (log(2))^(2*n), where c = 2^(-log(2)/2) = 0.7864497045594053649114085152934509198700275589579678941719548714254307448... - Vaclav Kotesovec, Jun 07 2019
MATHEMATICA
Table[Sum[StirlingS1[n, k]*(Sum[(j - 1)!*StirlingS2[k, j], {j, 1, k}])^2, {k, 1, n}]/(n-1)!, {n, 1, 20}] (* Vaclav Kotesovec, Jun 07 2019 *)
Table[-(-1)^n + Sum[StirlingS1[n, k]*PolyLog[1-k, 2]^2, {k, 2, n}]/(n-1)!, {n, 1, 20}] (* Vaclav Kotesovec, Jun 07 2019 *)
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Vladeta Jovovic, Sep 28 2006
STATUS
approved