A278142 Denominators of partial sums of a Ramanujan series converging to 2^(3/2)/(sqrt(Pi)*Gamma(3/4)^2) given in A278146.

1, 256, 1048576, 268435456, 17592186044416, 4503599627370496, 18446744073709551616, 4722366482869645213696, 4951760157141521099596496896, 1267650600228229401496703205376, 5192296858534827628530496329220096, 1329227995784915872903807060280344576, 87112285931760246646623899502532662132736

Offset

0,2

Comments

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

Links

G. C. Greubel, Table of n, a(n) for n = 0..100

Formula

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.

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

Example

See A278141.

Mathematica

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

Prog

(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

Crossrefs

Cf. A278141, A278146.

Sequence in context: A018877 A283803 A330483 * A013759 A283933 A016832

Adjacent sequences: A278139 A278140 A278141 * A278143 A278144 A278145

Keyword

nonn,frac,easy

Author

Wolfdieter Lang, Nov 14 2016

Status

approved