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A207323 a(n) = Sum_{k=0..n} k*A002893(k). 0
0, 3, 33, 312, 2868, 26133, 237147, 2146992, 19409064, 175287597, 1581968247, 14270061192, 128673729492, 1159919095227, 10453609519917, 94194476541312, 848633286566256, 7644719039897661, 68858679361873263, 620181110747360616, 5585301978207342396, 50297638075074093723, 452923691790915847653 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Table of n, a(n) for n=0..22.

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

FORMULA

Conjecture: n*(n-1)*a(n) +(-14*n^2+23*n-12)*a(n-1) +(52*n^2-151*n+120)*a(n-2) +3*(-22*n^2+79*n-72)*a(n-3) +27*(n-2)^2*a(n-4)=0. - R. J. Mathar, Nov 28 2013

MATHEMATICA

a[n_] := Sum[k Sum[Binomial[k, j]^2 Binomial[2j, j], {j, 0, k}], {k, 0, n}];

Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Oct 31 2018 *)

CROSSREFS

Sequence in context: A043038 A274264 A107127 * A135697 A226508 A097486

Adjacent sequences:  A207320 A207321 A207322 * A207324 A207325 A207326

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Feb 16 2012

STATUS

approved

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Last modified September 21 19:59 EDT 2019. Contains 327282 sequences. (Running on oeis4.)