A105796 "Stirling-Bernoulli transform" of Jacobsthal numbers.

0, 1, 1, 13, 25, 541, 1561, 47293, 181945, 7087261, 34082521, 1622632573, 9363855865, 526858348381, 3547114323481, 230283190977853, 1771884893993785, 130370767029135901, 1128511554418948441, 92801587319328411133, 892562598748128067705, 81124824998504073881821

Offset: 0

Author

Paul Barry, Apr 20 2005

Keywords

• easy
• nonn

Links

• Alois P. Heinz, Table of n, a(n) for n = 0..425

Crossrefs

Cf. A050946.

Programs

Maple

a:= n-> -add((-1)^k*k!*Stirling2(n+1, k+1)*(<<0|1>, <2|1>>^k)[1, 2], k=0..n):
seq(a(n), n=0..23);  # Alois P. Heinz, May 09 2018

Mathematica

CoefficientList[Series[E^x*(1-E^x)/((2-E^x)*(1-2*E^x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 26 2013 *)

Formula

E.g.f.: e^x*(1-e^x)/((2-e^x)*(1-2*e^x)).

a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * S2(n,k) * A001045(k).

a(n) ~ n! * (2-(-1)^n)/(6*log(2)^(n+1)). - Vaclav Kotesovec, Sep 26 2013

a(n) = Sum_{k = 0..n} (-1)^(n-k)*A131689(n,k)*A001045(k). - Philippe Deléham, May 25 2015