A335750 a(n) = numerator(Bernoulli(2*n)*(1/2 - n)! / sqrt(Pi)).

1, 1, 1, 2, 4, 8, 11056, 32, 231488, 5614976, 44700416, 39773696, 242036829184, 1347442688, 13896827482112, 14116194346606592, 126309515939299328, 4968569161351168, 1724597636500912693116928, 20212640119738990592, 68441268157533158650937344, 796968953534517505001259008

Offset: 0

Author

Peter Luschny, Jun 20 2020

Keywords

• nonn
• frac

Examples

			r(n) = 1/2, 1/6, 1/15, 2/63, 4/225, 8/693, 11056/1289925, 32/4455, ...
		

Crossrefs

Cf. A335751 (denominator), A000367/A002445, A004193.

Programs

Maple

a := n -> bernoulli(2*n)*(1/2 - n)! / sqrt(Pi):
seq(numer(simplify(a(n))), n = 0..21);

Formula

a(n) = numerator(-2*n*Zeta(1 - 2*n)*(1/2 - n)! / sqrt(Pi)) for n >= 1.