A278142 - OEIS

%I #17 Jan 11 2017 03:42:10

%S 1,256,1048576,268435456,17592186044416,4503599627370496,

%T 18446744073709551616,4722366482869645213696,

%U 4951760157141521099596496896,1267650600228229401496703205376,5192296858534827628530496329220096,1329227995784915872903807060280344576,87112285931760246646623899502532662132736

%N Denominators of partial sums of a Ramanujan series converging to 2^(3/2)/(sqrt(Pi)*Gamma(3/4)^2) given in A278146.

%C The numerators are given in A278141, where also details and a reference are given.

%H G. C. Greubel, <a href="/A278142/b278142.txt">Table of n, a(n) for n = 0..100</a>

%F a(n) = denominator(r(n)), with the rationals r(n) = Sum_{k=0..n} (1+8*k)*(risefac(-1/4,k)/k!)^4. The rising factorial is risefac(x,k) = Product_{j=0..k-1} (x+j), and risefac(x,0) = 1.

%F a(n) = denominator( Sum_{k=0..n} (1+8*k)*(binomial(-1/4,k))^4 ).

%e See A278141.

%t Denominator[Table[Sum[(1 + 8*k)*(Binomial[-1/4, k])^4, {k, 0, n}], {n, 0, 10}]] (* _G. C. Greubel_, Jan 10 2017 *)

%o (PARI) for (n = 0, 10, print1 (denominator(sum (k = 0, n, (1+8*k)*(binomial (-1/4, k))^4)), ", ")) \\ _G. C. Greubel_, Jan 10 2017

%Y Cf. A278141, A278146.

%K nonn,frac,easy

%O 0,2

%A _Wolfdieter Lang_, Nov 14 2016