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 A259459 From higher-order arithmetic progressions. 2
 1, 18, 360, 9000, 283500, 11113200, 533433600, 30862944000, 2121827400000, 171160743600000, 16020645600960000, 1722947613266880000, 211061082625192800000, 29223842209642080000000, 4542220046298654720000000 (list; graph; refs; listen; history; text; internal format)
 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: -2*n*a(n) +(n+3)*(n+2)^2*a(n-1)=0. - R. J. Mathar, Jul 15 2015 Conjecture: g.f.: 3F0(4,3,3;;x/2). - R. J. Mathar, Aug 09 2015 MAPLE rV := proc(n, a, d) n*(n+1)/2*a+(n-1)*n*(n+1)/6*d; end proc: A259459 := proc(n) mul(rV(i, a, d), i=1..n+1) ; coeftayl(%, d=0, 1) ; coeftayl(%, a=0, n) ; end proc: seq(A259459(n), n=1..15) ; # R. J. Mathar, Jul 14 2015 MATHEMATICA rV[n_, a_, d_] := n(n+1)/2*a + (n-1)n(n+1)/6*d; A259459[n_] := Product[rV[i, a, d], {i, 1, n+2}] // SeriesCoefficient[#, {d, 0, 1}]& // SeriesCoefficient[#, {a, 0, n+1}]&; Table[A259459[n], {n, 0, 14}] (* Jean-François Alcover, Apr 27 2023, after R. J. Mathar *) CROSSREFS Sequence in context: A182609 A320764 A086502 * A099276 A221348 A285400 Adjacent sequences: A259456 A259457 A259458 * A259460 A259461 A259462 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 30 2015 STATUS approved

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Last modified August 11 10:58 EDT 2024. Contains 375068 sequences. (Running on oeis4.)