OFFSET
0,1
LINKS
Karl Dienger, Beiträge zur Lehre von den arithmetischen und geometrischen Reihen höherer Ordnung, Jahres-Bericht Ludwig-Wilhelm-Gymnasium Rastatt, Rastatt, 1910. [Annotated scanned copy]
FORMULA
Conjecture: 3*n*a(n) +(-3*n^2-19*n-44)*a(n-1) -2*(n+2)^2*a(n-2)=0. - R. J. Mathar, Jul 15 2015
From Georg Fischer, Dec 06 2024: (Start)
a(n) = (n+3)!*(n+2)*(n+1)*(n+3)*(3*n+8)/96.
D-finite with recurrence: -n*(3*n+5)*a(n) + (n+3)^2*(3*n+8)*a(n-1) = 0. (End)
MAPLE
rX := proc(n, a, d)
n*a+(n-1)*n/2*d;
end proc:
A259457 := proc(n)
mul(rX(i, a, d), i=1..n+2) ;
coeftayl(%, d=0, 2) ;
coeftayl(%, a=0, n) ;
end proc:
seq(A259457(n), n=1..25) ; # R. J. Mathar, Jul 15 2015
MATHEMATICA
rX[n_, a_, d_] := n*a + (n-1)*n/2*d;
A259457[n_] :=
Product[rX[i, a, d], {i, 1, n+3}]//
SeriesCoefficient[#, {d, 0, 2}]&//
SeriesCoefficient[#, {a, 0, n+1}]&;
CROSSREFS
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 30 2015
STATUS
approved