OFFSET
0,3
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..408
FORMULA
E.g.f.: 1/(2 - x^2 - exp(x)).
a(n) ~ n! / ((2 + 2*r - r^2) * r^(n+1)), where r = A201752 = 0.5372744491738566... is the positive root of the equation 2 - r^2 - exp(r) = 0.
a(0) = a(1) = 1; a(n) = n * (n-1) * a(n-2) + Sum_{k=1..n} binomial(n,k) * a(n-k). - Seiichi Manyama, Mar 11 2022
MATHEMATICA
nmax = 20; CoefficientList[Normal[Series[1/(2-x^2-E^x), {x, 0, nmax}]], x] * Range[0, nmax]!
PROG
(PARI) my(x='x+O('x^25)); Vec(serlaplace(1/(2 - x^2 - exp(x)))) \\ Michel Marcus, Jul 12 2021
(PARI) b(n, m) = if(n==0, 1, sum(k=1, n, (1+(k==m)*m!)*binomial(n, k)*b(n-k, m)));
a(n) = b(n, 2); \\ Seiichi Manyama, Mar 12 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Vaclav Kotesovec, Jul 12 2021
STATUS
approved