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A259463 From higher-order arithmetic progressions. 1
5, 550, 61250, 8330000, 318084480000, 88994505600000, 311969750400000000, 13537335651840000000, 7186069008518400000000, 4614893517270516480000000, 3548831033950800998400000000, 3237226357799023349760000000000, 3472842105575052965314560000000000 (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*(3*n+5)*a(n) +(n+5)*(n+4)*(3*n+8)*(n+3)^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:

A259463 := proc(n)

        mul(rXI(i, a, d), i=1..n+2) ;

        coeftayl(%, d=0, 2) ;

        coeftayl(%, a=0, n) ;

end proc:

seq(A259463(n), n=1..25) ; # R. J. Mathar, Jul 15 2015

CROSSREFS

Sequence in context: A302470 A303252 A112900 * A241802 A274081 A153404

Adjacent sequences:  A259460 A259461 A259462 * A259464 A259465 A259466

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Jun 30 2015

STATUS

approved

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Last modified June 27 13:59 EDT 2022. Contains 354896 sequences. (Running on oeis4.)