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A105796 "Stirling-Bernoulli transform" of Jacobsthal numbers. 3
0, 1, 1, 13, 25, 541, 1561, 47293, 181945, 7087261, 34082521, 1622632573, 9363855865, 526858348381, 3547114323481, 230283190977853, 1771884893993785, 130370767029135901, 1128511554418948441, 92801587319328411133, 892562598748128067705, 81124824998504073881821 (list; graph; refs; listen; history; text; internal format)
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

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Last modified October 14 08:54 EDT 2019. Contains 327995 sequences. (Running on oeis4.)