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A278142 Denominators of partial sums of a Ramanujan series converging to 2^(3/2)/(sqrt(Pi)*Gamma(3/4)^2) given in A278146. 3
1, 256, 1048576, 268435456, 17592186044416, 4503599627370496, 18446744073709551616, 4722366482869645213696, 4951760157141521099596496896, 1267650600228229401496703205376, 5192296858534827628530496329220096, 1329227995784915872903807060280344576, 87112285931760246646623899502532662132736 (list; graph; refs; listen; history; text; internal format)
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

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Last modified April 18 15:51 EDT 2021. Contains 343089 sequences. (Running on oeis4.)