|
|
A352327
|
|
Expansion of e.g.f.: 1/(3 - exp(x) - cosh(x)).
|
|
3
|
|
|
1, 1, 4, 19, 130, 1081, 10894, 127639, 1711210, 25798141, 432212134, 7964801659, 160121522290, 3487254825601, 81790592435374, 2055350489070079, 55093108433421370, 1569052795651631461, 47315282424232826614, 1506074331671551028899
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,3
|
|
LINKS
|
|
|
FORMULA
|
a(0) = 1; a(n) = Sum_{k=1..n} (3+(-1)^k)/2 * binomial(n,k) * a(n-k).
a(n) ~ n! / (sqrt(6) * log(1 + sqrt(2/3))^(n+1)). - Vaclav Kotesovec, Mar 12 2022
|
|
MAPLE
|
a:= proc(n) option remember; `if`(n=0, 1, add(
a(n-k)*binomial(n, k)*(2-(k mod 2)), k=1..n))
end:
|
|
MATHEMATICA
|
m = 19; Range[0, m]! * CoefficientList[Series[1/(3 - Exp[x] - Cosh[x]), {x, 0, m}], x] (* Amiram Eldar, Mar 12 2022 *)
|
|
PROG
|
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(3-exp(x)-cosh(x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, (3+(-1)^k)/2*binomial(n, k)*a(n-k)));
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|