OFFSET
0,4
COMMENTS
Transform of binomial(1,n) under the matrix A119879.
LINKS
Robert Israel, Table of n, a(n) for n = 0..480
FORMULA
a(n) = Sum_{k=0..n} A119879(n,k)*C(1,k).
E.g.f.: (1+x)/sech(x) = (1+x)*(1 - x^2/Q(0)), where Q(k) = (2*k+1)*(2*k+2) + x^2 - (2*k+1)*(2*k+2)*x^2/Q(k+1) ; (continued fraction). - Sergei N. Gladkovskii, Dec 06 2013
a(n) = EulerE[n] + n*EulerE[n-1], n>0. - Benedict W. J. Irwin, May 30 2016
MAPLE
seq(`if`(n::odd, n*euler(n-1), euler(n)), n=0..24); # Peter Luschny, May 30 2016
MATHEMATICA
Table[EulerE[n] + n*EulerE[n-1], {n, 20}] (* Benedict W. J. Irwin, May 30 2016 *)
PROG
(PARI) Vec(serlaplace((1+x)/cosh(x + O(x^30)))) \\ Andrew Howroyd, Feb 27 2018
(Magma) R<x>:=PowerSeriesRing(Rationals(), 30); Coefficients(R!(Laplace( (1+x)/Cosh(x) ))); // G. C. Greubel, Jun 07 2023
(SageMath)
def A119882(n): return n*euler_number(n-1) if n%2==1 else euler_number(n)
[A119882(n) for n in range(41)] # G. C. Greubel, Jun 07 2023
CROSSREFS
KEYWORD
easy,sign
AUTHOR
Paul Barry, May 26 2006
STATUS
approved