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

Author

Paul Barry, Apr 20 2005

Keywords

• nonn
• easy

Crossrefs

Cf. A050946.

Programs

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 *)

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