A105797 "Stirling-Bernoulli transform" of Pell numbers.

0, 1, 3, 19, 135, 1291, 14343, 188539, 2815095, 47412811, 886239783, 18231365659, 409053408855, 9943622273131, 260300948527623, 7300927107288379, 218426614502831415, 6943261704033434251, 233692323131307301863

Offset

0,3

Links

Table of n, a(n) for n=0..18.

Formula

E.g.f.: e^x*(1-e^x)/(1-4*e^x+2*e^(2*x)).

a(n) = Sum_{k = 0..n} (-1)^(n-k) * k! * S2(n, k) * A000129(k).

a(n) ~ n!/(4*log(1+1/sqrt(2))^(n+1)). - Vaclav Kotesovec, Sep 26 2013

a(n) = Sum_{k = 0..n} (-1)^(n-k) * A131689(n,k) * A000129(k). - Philippe Deléham, May 25 2015

Mathematica

CoefficientList[Series[E^x*(1-E^x)/(1-4*E^x+2*E^(2*x)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 26 2013 *)

Crossrefs

Cf. A050946.

Sequence in context: A305550 A035086 A215852 * A278189 A221297 A138513

Adjacent sequences: A105794 A105795 A105796 * A105798 A105799 A105800

Keyword

nonn,easy

Author

Paul Barry, Apr 20 2005

Status

approved