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A259462
From higher-order arithmetic progressions.
3
1, 30, 1200, 70000, 5880000, 691488000, 110638080000, 23471078400000, 6454546560000000, 2256222608640000000, 985518035453952000000, 529939925428193280000000, 346227417946419609600000000, 271655358696421539840000000000, 253338025938605687439360000000000, 278215820085776765945905152000000000, 356811789260008702325623357440000000000
OFFSET
0,2
COMMENTS
"3 over n!" in Dienger's article is A087047. A_1 is A000217. - Georg Fischer, Dec 16 2024
LINKS
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
D-finite with recurrence: -6*n*a(n) +(n+4)*(n+3)*(n+2)^2*a(n-1)=0. - R. J. Mathar, Jul 15 2015
a(n) = 2^(-n-3)*3^(-n-2)*(n+2)!*(n+3)!*(n+4)!/4*(n+2)*(n+1)/2. - Georg Fischer, Dec 16 2024
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
KEYWORD
nonn
AUTHOR
N. J. A. Sloane, Jun 30 2015
STATUS
approved