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%I #15 May 09 2018 19:11:42
%S 0,1,1,13,25,541,1561,47293,181945,7087261,34082521,1622632573,
%T 9363855865,526858348381,3547114323481,230283190977853,
%U 1771884893993785,130370767029135901,1128511554418948441,92801587319328411133,892562598748128067705,81124824998504073881821
%N "Stirling-Bernoulli transform" of Jacobsthal numbers.
%H Alois P. Heinz, <a href="/A105796/b105796.txt">Table of n, a(n) for n = 0..425</a>
%F E.g.f.: e^x*(1-e^x)/((2-e^x)*(1-2*e^x)).
%F a(n) = Sum_{k=0..n} (-1)^(n-k) * k! * S2(n,k) * A001045(k).
%F a(n) ~ n! * (2-(-1)^n)/(6*log(2)^(n+1)). - _Vaclav Kotesovec_, Sep 26 2013
%F a(n) = Sum_{k = 0..n} (-1)^(n-k)*A131689(n,k)*A001045(k). - _Philippe Deléham_, May 25 2015
%p a:= n-> -add((-1)^k*k!*Stirling2(n+1, k+1)*(<<0|1>, <2|1>>^k)[1, 2], k=0..n):
%p seq(a(n), n=0..23); # _Alois P. Heinz_, May 09 2018
%t 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 *)
%Y Cf. A050946.
%K easy,nonn
%O 0,4
%A _Paul Barry_, Apr 20 2005
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