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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:
seq(a(n), n=0..19); # Alois P. Heinz, Mar 25 2022
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
Sequence in context: A366182 A330494 A352306 * A305867 A121681 A135742
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 12 2022
STATUS
approved

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Last modified March 3 04:18 EST 2024. Contains 370499 sequences. (Running on oeis4.)