A207321 Partial sums of A002893.

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

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

Mathematica

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

Crossrefs

Sequence in context: A114311 A134092 A000274 * A193236 A357203 A215047

Adjacent sequences: A207318 A207319 A207320 * A207322 A207323 A207324

Keyword

nonn

Author

N. J. A. Sloane, Feb 16 2012

Status

approved