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A294984 Number of compositions (ordered partitions) of 1 into exactly 5n+1 powers of 1/(n+1). 2
1, 525, 487630, 709097481, 1303699790001, 2713420774885145, 6078597035484932995, 14303426764164190428105, 34883776613634643730481238, 87451065686506297464527100009, 224099040671253218432160498959100, 584668421756097333754383886118155275 (list; graph; refs; listen; history; text; internal format)
OFFSET
0,2
LINKS
FORMULA
a(n) ~ 5^(5*n + 3/2) / (4 * Pi^2 * n^2). - Vaclav Kotesovec, Sep 20 2019
MAPLE
b:= proc(n, r, p, k) option remember;
`if`(n<r, 0, `if`(r=0, `if`(n=0, p!, 0), add(
b(n-j, k*(r-j), p+j, k)/j!, j=0..min(n, r))))
end:
a:= n-> (k-> `if`(n=0, 1, b(k*n+1, 1, 0, n+1)))(5):
seq(a(n), n=0..15);
MATHEMATICA
b[n_, r_, p_, k_] := b[n, r, p, k] = If[n < r, 0, If[r == 0, If[n == 0, p!, 0], Sum[b[n - j, k*(r - j), p + j, k]/j!, {j, 0, Min[n, r]}]]];
a[n_] := If[n == 0, 1, b[#*n + 1, 1, 0, n + 1]]&[5];
Table[a[n], {n, 0, 15}] (* Jean-François Alcover, May 21 2018, translated from Maple *)
CROSSREFS
Row n=5 of A294746.
Sequence in context: A217742 A204692 A168308 * A020379 A251022 A251108
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Nov 12 2017
STATUS
approved

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Last modified April 18 12:53 EDT 2024. Contains 371780 sequences. (Running on oeis4.)