|
|
A111196
|
|
a(n) = 2^(-n)*Sum_{k=0..n} binomial(2*n+1, 2*k+1)*A000364(n-k).
|
|
0
|
|
|
1, 2, 9, 78, 1141, 25442, 804309, 34227438, 1886573641, 130746521282, 11127809595009, 1141012634368398, 138730500808639741, 19735099323279743522, 3247323803322747092109, 611982206046097666022958
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
a(n) ~ sinh(Pi/2) * 2^(3*n + 5) * n^(2*n + 3/2) / (Pi^(2*n + 3/2) * exp(2*n)). - Vaclav Kotesovec, Jul 10 2021
|
|
MATHEMATICA
|
t = Range[0, 32]!CoefficientList[ Series[ Sec[x], {x, 0, 32}], x]; f[n_] := 2^(-n)*Sum [Binomial[2n + 1, 2k + 1]*t[[2n - 2k + 1]], {k, 0, n}]; Table[ f[n], {n, 0, 16}] (* Robert G. Wilson v, Oct 24 2005 *)
Table[Sum[Binomial[2*n + 1, 2*k + 1]*Abs[EulerE[2*(n-k)]], {k, 0, n}] / 2^n, {n, 0, 20}] (* Vaclav Kotesovec, Jul 10 2021 *)
|
|
CROSSREFS
|
|
|
KEYWORD
|
easy,nonn
|
|
AUTHOR
|
|
|
EXTENSIONS
|
|
|
STATUS
|
approved
|
|
|
|