A259460 From higher-order arithmetic progressions.

4, 220, 10500, 535500, 30870000, 2044828800, 156029328000, 13673998800000, 1369285948800000, 155756276676000000, 20005336176265440000, 2884501462544301600000, 464334381775424160000000, 83021688624014300160000000, 16408769917253890176000000000, 3569104362241728159962112000000, 850861011640079911341911040000000

Offset

0,1

Links

Table of n, a(n) for n=0..16.

Karl Dienger, Beiträge zur Lehre von den arithmetischen und geometrischen Reihen höherer Ordnung, Jahres-Bericht Ludwig-Wilhelm-Gymnasium Rastatt, Rastatt, 1910. [Annotated scanned copy]

Maple

rV := proc(n, a, d)
    n*(n+1)/2*a+(n-1)*n*(n+1)/6*d;
end proc:
A259460 := proc(n)
    mul(rV(i, a, d), i=1..n+2) ;
    coeftayl(%, d=0, 2) ;
    coeftayl(%, a=0, n) ;
end proc:
seq(A259460(n), n=1..18) ; # R. J. Mathar, Jul 14 2015

Mathematica

rV[n_, a_, d_] := n (n + 1)/2*a + (n - 1) n (n + 1)/6*d;
A259460[n_] :=
   Product[rV[i, a, d], {i, 1, n + 3}] //
   SeriesCoefficient[#, {d, 0, 2}] & //
   SeriesCoefficient[#, {a, 0, n + 1}] & ;
Table[A259460[n], {n, 0, 16}] (* Jean-François Alcover, Apr 27 2023, after R. J. Mathar *)

Crossrefs

Sequence in context: A078693 A222421 A025420 * A227822 A052209 A211610

Adjacent sequences: A259457 A259458 A259459 * A259461 A259462 A259463

Keyword

nonn

Author

N. J. A. Sloane, Jun 30 2015

Extensions

Typos in data corrected by Jean-François Alcover, Apr 27 2023

Status

approved