OFFSET
0,4
COMMENTS
Transform of n! under the matrix A119879.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..445
FORMULA
a(n) = Sum_{k=0..n} A119879(n,k) * k!.
E.g.f.: 1/U(0) where U(k) = 1 - x/(1 - x/(x - (2*k+1)*(2*k+2)/U(k+1)); (continued fraction, 3-step). - Sergei N. Gladkovskii, Oct 17 2012
a(n) ~ n! * 2*exp(1)/(exp(2)+1). - Vaclav Kotesovec, Sep 25 2013
a(n) = n! * Sum_{j=0..n} A122045(j)/j!. - G. C. Greubel, Jun 07 2023
MAPLE
restart: G(x):= sech(x)/(1-x): f[0]:=G(x): for n from 1 to 21 do f[n]:=diff(f[n-1], x) od: x:=0: seq(f[n], n=0..20); # Zerinvary Lajos, Apr 03 2009
MATHEMATICA
CoefficientList[Series[1/((1-x)*(E^x/2+E^(-x)/2)), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Sep 25 2013 *)
Table[n!*Sum[EulerE[j]/j!, {j, 0, n}], {n, 0, 40}] (* G. C. Greubel, Jun 07 2023 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( 1/((1-x)*Cosh(x)) ))); // G. C. Greubel, Jun 07 2023
(SageMath)
def A119884(n): return factorial(n)*sum(euler_number(j)/factorial(j) for j in range(n+1))
[A119884(n) for n in range(41)] # G. C. Greubel, Jun 07 2023
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
Paul Barry, May 26 2006
STATUS
approved