|
|
A259462
|
|
From higher-order arithmetic progressions.
|
|
1
|
|
|
1, 30, 1200, 70000, 5880000, 691488000, 110638080000, 23471078400000, 6454546560000000, 2256222608640000000, 985518035453952000000, 529939925428193280000000, 346227417946419609600000000, 271655358696421539840000000000, 253338025938605687439360000000000
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
OFFSET
|
0,2
|
|
LINKS
|
|
|
FORMULA
|
Conjecture: -6*n*a(n) +(n+4)*(n+3)*(n+2)^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:
mul(rXI(i, a, d), i=1..n+1) ;
coeftayl(%, d=0, 1) ;
coeftayl(%, a=0, n) ;
end proc:
|
|
MATHEMATICA
|
rXI[n_, a_, d_] := n(n+1)(n+2)/6*a + (n+2)(n+1)n(n-1)/24*d;
Product[rXI[i, a, d], {i, 1, n + 2}] //
SeriesCoefficient[#, {d, 0, 1}] & //
SeriesCoefficient[#, {a, 0, n + 1}] & ;
|
|
CROSSREFS
|
|
|
KEYWORD
|
nonn
|
|
AUTHOR
|
|
|
STATUS
|
approved
|
|
|
|