OFFSET
0,5
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..800
FORMULA
a(0) = 0; a(n) = n!! - Sum_{k=1..n-1} k!!*a(n-k).
MATHEMATICA
nmax = 28; CoefficientList[Series[1 - 1/Sum[k!! x^k, {k, 0, nmax}], {x, 0, nmax}], x]
a[0] = 0; a[n_]:= a[n] = n!! - Sum[k!! a[n-k], {k, n-1}];
Table[a[n], {n, 0, 28}]
PROG
(Magma)
m:=80;
F2:= func< n | n mod 2 eq 0 select Round(2^(n/2)*Gamma(n/2+1)) else Round( Gamma((n+3)/2)*Binomial(n+1, Floor((n+1)/2))/2^((n+1)/2) ) >;
R<x>:=PowerSeriesRing(Rationals(), m);
[0] cat Coefficients(R!( 1 - 1/(&+[F2(j)*x^j : j in [0..m+2]]) )); // G. C. Greubel, Jan 24 2024
(SageMath)
from sympy import factorial2
m=80;
def f(x): return 1 - 1/sum(factorial2(k)*x^k for k in range(m+1))
def A307063_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( f(x) ).list()
A307063_list(m) # G. C. Greubel, Jan 24 2024
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Mar 21 2019
STATUS
approved