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 A241756 A finite sum of products of binomial coefficients: Sum_(m=0..n) binomial(-1/4, m)^2*binomial(-1/4, n-m)^2 (C. C. Grosjean's problem, denominators). 7
 1, 8, 512, 4096, 2097152, 16777216, 1073741824, 8589934592, 35184372088832, 281474976710656, 18014398509481984, 144115188075855872, 73786976294838206464, 590295810358705651712, 37778931862957161709568, 302231454903657293676544 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS This sequence seems to appear also  as denominators of A277232, A277234, and A278143. - Wolfdieter Lang, Nov 16 2016 REFERENCES E. S. Andersen and M. E. Larsen. A finite sum of products of binomial coefficients, Problem 92-18, by C. C. Grosjean, Solution. SIAM Rev. 35 (1993), 645-646. LINKS P. Flajolet, B. Salvy, and Helmut Prodinger, A Finite Sum of Products of Binomial Coefficients, Problem 92-18 by C. C. Grosjean, Solution. SIAM Rev. 35 (1993), 645-646. C. C. Grosjean, Problem no. 92-18, SIAM Rev. 34 (1992), p. 649. M. E. Larsen, Summa Summarum, page 114. FORMULA GAMMA(3/4)^2 * 4F3(1/4, 1/4, -n, -n; 1, 3/4-n, 3/4-n; 1)/(GAMMA(3/4-n)^2*GAMMA(n+1)^2). binomial(2n, n)^2*binomial(n-1/2, 2n)*(-1/4)^n. MATHEMATICA a[n_] := Binomial[2*n, n]^2*Binomial[n-1/2, 2*n]*(-1/4)^n; Table[a[n]//Denominator, {n, 0, 20}] CROSSREFS Cf. A241755, A277232, A277234, A278143. Sequence in context: A236077 A061460 A016935 * A236220 A128794 A195804 Adjacent sequences:  A241753 A241754 A241755 * A241757 A241758 A241759 KEYWORD nonn,frac AUTHOR Jean-François Alcover, Apr 28 2014 STATUS approved

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Last modified April 18 07:11 EDT 2021. Contains 343072 sequences. (Running on oeis4.)