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

0,4

Links

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

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

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 *)

Crossrefs

Cf. A050946.

Sequence in context: A295794 A122003 A123827 * A226051 A238338 A040156

Adjacent sequences: A105793 A105794 A105795 * A105797 A105798 A105799

Keyword

easy,nonn

Author

Paul Barry, Apr 20 2005

Status

approved