A077595 Numerator of integral from 0 to 1 of (1 + x^2)^n, in lowest terms.

1, 4, 28, 96, 1328, 4672, 33472, 121856, 3597056, 13417472, 33655808, 127508480, 5829259264, 22308732928, 171393728512, 660468137984, 40831182635008, 22589996269568, 175323994652672, 681560447647744, 10614717931323392, 289707123275726848, 2261982330593738752

Offset: 0

Author

Michael Somos, Nov 06 2002

Keywords

• nonn

Examples

			For n=3 the integral is 96/35, so a(3) = 96.
		

Crossrefs

Cf. A076729.

Programs

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 *)

PARI

{a(n) = if( n<0, 0, numerator( subst( intformal((1 + x^2)^n), x, 1)))}

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)