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 A294832 Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 4) = 2*A005476(k+1), for k >= 0. 2

%I #12 Nov 27 2017 11:37:58

%S 4,36,252,1197,47880,1388520,23604840,153431460,843873030,2953555605,

%T 17721333630,2091117368340,33457877893440,769531191549120,

%U 28472654087317440,2249339672898077760,2249339672898077760,200191230887928920640,9408987851732659270080,1881797570346531854016

%N Denominators of the partial sums of the reciprocals of the numbers (k + 1)*(5*k + 4) = 2*A005476(k+1), for k >= 0.

%C The corresponding numerators are given in A294831. Details are found there.

%F a(n) = denominator(V(5,4;n)) with V(5,4;n) = Sum_{k=0..n} 1/((k + 1)*(5*k + 4)) = Sum_{k=0..n} 1/(2*A005476(k+1)) = Sum_{k=0..n} (1/(k + 4/5) - 1/(k+1)).

%F For this sum in terms of the digamma function Psi see A294831.

%e For the rationals V(5,4;n) see A294831.

%o (PARI) a(n) = denominator(sum(k=0, n, 1/((k + 1)*(5*k + 4)))); \\ _Michel Marcus_, Nov 19 2017

%Y Cf. 2*A005476, A294831.

%K nonn,frac,easy

%O 0,1

%A _Wolfdieter Lang_, Nov 18 2017

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Last modified August 11 13:56 EDT 2024. Contains 375069 sequences. (Running on oeis4.)