A280655 Numerator of (Sum_{k=0..n^2-1} (-1)^k*sqrt(Pi)/(Gamma(1/2-k)*Gamma(1+k))) - n.

0, 3, 11091, 32104739, 43189424229655, 110209500084824275641, 17401090686295157740521962087, 1341749054684714449837337405947519267, 416437630008271514606815213642830281374740126189, 31880038884855523088456476438831355463732624957105297113285

Offset: 1

Author

Ralf Steiner, Apr 12 2017

Keywords

• nonn
• frac

Comments

a(n) has at most n prime factors.

Crossrefs

Cf. A280656 (denominators), A285388.

Programs

Mathematica

Numerator[Table[Sum[Binomial[2k,k]/4^k,{k,0,n^2-1}]-n,{n,1,10}]]

Formula

a(n)=Numerator of Sum_{k=0..n^2-1}(Binomial(2k,k)/4^k)-n.