A277585 Denominator of Sum_{k=0..n} (2^k * (k!)^2)/(2k + 1)!.
1, 3, 15, 21, 315, 3465, 45045, 15015, 765765, 14549535, 14549535, 25741485, 1673196525, 1003917915, 145568097675, 265447707525, 1504203675975, 4512611027925, 166966608033225, 33393321606645, 1369126185872445, 58872425992515135, 294362129962575675
Offset: 0
Examples
b(0) = 1, so a(0) = 1. b(1) = 4/3, so a(1) = 3. b(2) = 22/15, so a(2) = 15. b(3) = 32/21, so a(3) = 21. b(4) = 488/315, so a(4) = 315.
Links
- Seiichi Manyama, Table of n, a(n) for n = 0..1154
- Eric Weisstein's World of Mathematics, Pi Formulas
Programs
-
PARI
a(n) = denominator(sum(k=0, n, (2^k * (k!)^2)/(2*k + 1)!)); \\ Michel Marcus, Oct 22 2016
Formula
a(n) = denominator(Sum_{k=0..n} (2^k)/A002457(k)).
Comments