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

1,2

Comments

a(n) has at most n prime factors.

Links

Table of n, a(n) for n=1..10.

Formula

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

Mathematica

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

Crossrefs

Cf. A280656 (denominators), A285388.

Sequence in context: A280300 A375690 A171363 * A262651 A309246 A055379

Adjacent sequences: A280652 A280653 A280654 * A280656 A280657 A280658

Keyword

nonn,frac

Author

Ralf Steiner, Apr 12 2017

Status

approved