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A207321

Partial sums of A002893 with A002893(0)=0.

0, 3, 18, 111, 750, 5403, 40572, 313407, 2471166, 19791003, 160459068, 1313922063, 10847561088, 90174127683, 754009158018, 6336733626111, 53489159252670, 453258909448635, 3854034482891724, 32871004555812111, 281127047928811200, 2410285909684370787, 20711470169495359602, 178337708176330555839

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OFFSET

0,2

LINKS

Table of n, a(n) for n=0..23.

Z.-W. Sun, Congruences for Franel numbers, arXiv preprint arXiv:1112.1034, 2011.

FORMULA

n^2*a(n) +(-11*n^2+10*n-3)*a(n-1) +(19*n^2-28*n+12)*a(n-2) -9*(n-1)^2*a(n-3)=0. - R. J. Mathar, Aug 25 2013

a(n) ~ 3^(2*n + 7/2) / (32*Pi*n). - Vaclav Kotesovec, Mar 30 2018

a(n) = A174123(n) - 1. - Sean A. Irvine, Jan 12 2025

MATHEMATICA

Table[Sum[HypergeometricPFQ[{1/2, -k, -k}, {1, 1}, 4], {k, 1, n}], {n, 0, 20}] (* Vaclav Kotesovec, Mar 30 2018 *)