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 A259464 From higher-order arithmetic progressions. 1
 75, 21875, 5512500, 1512630000, 484041600000, 184834742400000, 84715923600000000, 46534591303200000000, 30489464221856640000000, 23681690417572387200000000, 21660852835272876825600000000, 23175597788788462617600000000000, 28817200450516396946227200000000000 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,1 LINKS Table of n, a(n) for n=0..12. 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*(n+2)*a(n) +(n+6)*(n+5)*(n+4)^3*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: A259464 := proc(n) mul(rXI(i, a, d), i=1..n+3) ; coeftayl(%, d=0, 3) ; coeftayl(%, a=0, n) ; end proc: seq(A259464(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; A259464[n_] := Product[rXI[i, a, d], {i, 1, n+4}]// SeriesCoefficient[#, {d, 0, 3}]&// SeriesCoefficient[#, {a, 0, n+1}]&; Table[A259464[n], {n, 0, 12}] (* Jean-François Alcover, Apr 26 2023, after R. J. Mathar *) CROSSREFS Sequence in context: A361282 A093275 A251242 * A116527 A263064 A085404 Adjacent sequences: A259461 A259462 A259463 * A259465 A259466 A259467 KEYWORD nonn AUTHOR N. J. A. Sloane, Jun 30 2015 STATUS approved

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Last modified September 11 23:02 EDT 2024. Contains 375842 sequences. (Running on oeis4.)