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A352293
Expansion of e.g.f. 1/(2 - exp(x) - x/(1 + x)).
3
1, 2, 7, 43, 335, 3301, 38925, 535851, 8429139, 149173321, 2933274593, 63446532271, 1497102036567, 38269877372637, 1053531222709269, 31074273060116083, 977649690943993979, 32680936703516606737, 1156722832021068313833, 43216064601701505904983
OFFSET
0,2
LINKS
FORMULA
a(0) = 1; a(n) = Sum_{k=1..n} ((-1)^(k-1) * k! + 1) * binomial(n,k) * a(n-k).
a(n) ~ n! * (1+r)^2 / ((3 + r*(3+r)) * r^(n+1)), where r = 0.50855472406037552... is the root of the equation 2 - exp(r) - r/(1+r) = 0. - Vaclav Kotesovec, Jul 25 2022
MATHEMATICA
m = 19; Range[0, m]! * CoefficientList[Series[1/(2 - Exp[x] - x/(1 + x)), {x, 0, m}], x] (* Amiram Eldar, Mar 11 2022 *)
PROG
(PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(x)-x/(1+x))))
(PARI) a(n) = if(n==0, 1, sum(k=1, n, ((-1)^(k-1)*k!+1)*binomial(n, k)*a(n-k)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Seiichi Manyama, Mar 11 2022
STATUS
approved