cp's OEIS Frontend

a(n) = Sum_{k=0..n} Stirling2(n,k) * A015128(k) * k!.

a(n) ~ n! * exp(Pi^2 * (1 - log(2)) / (16*log(2)) + Pi * sqrt(n/(2*log(2)))) / (8*n*(log(2))^n).

a(n) = Sum_{k=0..n} Stirling2(n,k) * A156616(k) * k!.

a(n) ~ n! * exp(3 * (7*Zeta(3))^(1/3) * n^(2/3) / (4 * log(2)^(2/3)) + (1 - log(2)) * (7*Zeta(3))^(2/3) * n^(1/3) / (8 * log(2)^(4/3)) - 7*(log(2)^2 + log(2) - 1) * Zeta(3) / (48 * log(2)^2) + 1/12) * (7*Zeta(3))^(7/36) / (A * 2^(13/12) * sqrt(3*Pi) * n^(25/36) * (log(2))^(n + 11/36)), where A is the Glaisher-Kinkelin constant A074962. - Vaclav Kotesovec, Jun 22 2018

E.g.f.: -Sum_{k>=1} k * log(1 - (exp(x) - 1)^k).

E.g.f.: A(x) = log(B(x)), where B(x) = e.g.f. of A306046.

G.f.: Sum_{k>=1} (k - 1)! * sigma_2(k) * x^k / Product_{j=1..k} (1 - j*x), where sigma_2 = A001157.

exp(Sum_{n>=1} a(n) * log(1 + x)^n / n!) = g.f. of A000219.

a(n) = Sum_{k=1..n} Stirling2(n,k) * (k - 1)! * sigma_2(k).

a(n) ~ n! * zeta(3) * n / (4 * (log(2))^(n+2)). - Vaclav Kotesovec, Dec 15 2019

a(n) = Sum_{k=0..n} Stirling2(n,k) * A026007(k) * k!.

a(n) ~ n! * exp(3^(4/3) * Zeta(3)^(1/3) * n^(2/3) / (4 * log(2)^(2/3)) + (1 - log(2)) * (3*Zeta(3))^(2/3) * n^(1/3) / (8 * log(2)^(4/3)) - (log(2)^2 + log(2) - 1) * Zeta(3) / (16 * log(2)^2)) * Zeta(3)^(1/6) / (2^(13/12) * 3^(1/3) * sqrt(Pi) * n^(2/3) * (log(2))^(n + 1/3)). - Vaclav Kotesovec, Jun 23 2018