OFFSET
0,2
FORMULA
From Fabian Pereyra, Aug 16 2024: (Start)
a(n) = numerator(Sum_{k=0..n} binomial(n,k)/(2*k+1)).
E.g.f.: Sum_{x>=0} a(n)/A001803(n)*x^n/n! = Integral_{z=0..1} e^(x*(1+z^2)) dz. (End)
EXAMPLE
For n=3 the integral is 96/35, so a(3) = 96.
MATHEMATICA
a[n_] := Numerator[Integrate[(1 + x x)^n, {x, 0, 1}]]
a[n_] := Hypergeometric2F1[-n, 1/2, 3/2, -1]
Table[Numerator[a[n]], {n, 0, 20}] (* Gerry Martens, Aug 09 2015 *)
PROG
(PARI) {a(n) = if( n<0, 0, numerator( subst( intformal((1 + x^2)^n), x, 1)))}
CROSSREFS
KEYWORD
nonn
AUTHOR
Michael Somos, Nov 06 2002
STATUS
approved