A259462 From higher-order arithmetic progressions.

1, 30, 1200, 70000, 5880000, 691488000, 110638080000, 23471078400000, 6454546560000000, 2256222608640000000, 985518035453952000000, 529939925428193280000000, 346227417946419609600000000, 271655358696421539840000000000, 253338025938605687439360000000000

Offset

0,2

Links

Table of n, a(n) for n=0..14.

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: -6*n*a(n) +(n+4)*(n+3)*(n+2)^2*a(n-1)=0. - R. J. Mathar, Jul 15 2015

Maple

rXI := proc(n, a, d)
        n*(n+1)*(n+2)/6*a+(n+2)*(n+1)*n*(n-1)/24*d;
end proc:
A259462 := proc(n)
        mul(rXI(i, a, d), i=1..n+1) ;
        coeftayl(%, d=0, 1) ;
        coeftayl(%, a=0, n) ;
end proc:
seq(A259462(n), n=1..25) ; # R. J. Mathar, Jul 15 2015

Mathematica

rXI[n_, a_, d_] := n(n+1)(n+2)/6*a + (n+2)(n+1)n(n-1)/24*d;
A259462[n_] :=
   Product[rXI[i, a, d], {i, 1, n + 2}] //
   SeriesCoefficient[#, {d, 0, 1}] & //
   SeriesCoefficient[#, {a, 0, n + 1}] & ;
Table[A259462[n], {n, 0, 14}] (* Jean-François Alcover, Apr 27 2023, after R. J. Mathar *)

Crossrefs

Sequence in context: A075187 A265101 A214820 * A269682 A269471 A060076

Adjacent sequences: A259459 A259460 A259461 * A259463 A259464 A259465

Keyword

nonn

Author

N. J. A. Sloane, Jun 30 2015

Status

approved