OFFSET
0,3
LINKS
Robert Israel, Table of n, a(n) for n = 0..426
FORMULA
a(0) = a(1) = 1; a(n) = n * (a(n-1) + (n-1) * a(n-2) / 2) + Sum_{k=4..n} binomial(n,k) * a(n-k).
MAPLE
S:= series(1/(2+x^3/6-exp(x)), x, 31):
seq(coeff(S, x, i)*i!, i=0..30); # Robert Israel, Aug 28 2020
MATHEMATICA
nmax = 20; CoefficientList[Series[1/(2 + x^3/6 - Exp[x]), {x, 0, nmax}], x] Range[0, nmax]!
a[0] = a[1] = 1; a[n_] := a[n] = n (a[n - 1] + (n - 1) a[n - 2]/2) + Sum[Binomial[n, k] a[n - k], {k, 4, n}]; Table[a[n], {n, 0, 20}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Aug 13 2020
STATUS
approved