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%I #14 Apr 27 2023 09:11:09
%S 1,18,360,9000,283500,11113200,533433600,30862944000,2121827400000,
%T 171160743600000,16020645600960000,1722947613266880000,
%U 211061082625192800000,29223842209642080000000,4542220046298654720000000
%N From higher-order arithmetic progressions.
%H Karl Dienger, <a href="/A000217/a000217.pdf">Beiträge zur Lehre von den arithmetischen und geometrischen Reihen höherer Ordnung</a>, Jahres-Bericht Ludwig-Wilhelm-Gymnasium Rastatt, Rastatt, 1910. [Annotated scanned copy]
%F Conjecture: -2*n*a(n) +(n+3)*(n+2)^2*a(n-1)=0. - _R. J. Mathar_, Jul 15 2015
%F Conjecture: g.f.: 3F0(4,3,3;;x/2). - _R. J. Mathar_, Aug 09 2015
%p rV := proc(n,a,d)
%p n*(n+1)/2*a+(n-1)*n*(n+1)/6*d;
%p end proc:
%p A259459 := proc(n)
%p mul(rV(i,a,d),i=1..n+1) ;
%p coeftayl(%,d=0,1) ;
%p coeftayl(%,a=0,n) ;
%p end proc:
%p seq(A259459(n),n=1..15) ; # _R. J. Mathar_, Jul 14 2015
%t rV[n_, a_, d_] := n(n+1)/2*a + (n-1)n(n+1)/6*d;
%t A259459[n_] :=
%t Product[rV[i, a, d], {i, 1, n+2}] //
%t SeriesCoefficient[#, {d, 0, 1}]& //
%t SeriesCoefficient[#, {a, 0, n+1}]&;
%t Table[A259459[n], {n, 0, 14}] (* _Jean-François Alcover_, Apr 27 2023, after _R. J. Mathar_ *)
%K nonn
%O 0,2
%A _N. J. A. Sloane_, Jun 30 2015
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