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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
OFFSET
0,2
LINKS
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-François Alcover, Oct 31 2018 *)
CROSSREFS
Sequence in context: A043038 A274264 A107127 * A135697 A226508 A097486
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Feb 16 2012
STATUS
approved