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A294988 Number of compositions (ordered partitions) of 1 into exactly 9n+1 powers of 1/(n+1).

%I A294988 #10 Sep 20 2019 05:07:34
%S A294988 1,5259885,121218250616173,8684483842898500680225,
%T A294988 1085776473843765315524916060126,
%U A294988 179835209135492330050411858875313971595,34994508245963099403565066291175900528344592700,7565469782615095731665958935875509379368611893407583633
%N A294988 Number of compositions (ordered partitions) of 1 into exactly 9n+1 powers of 1/(n+1).
%H A294988 Alois P. Heinz, <a href="/A294988/b294988.txt">Table of n, a(n) for n = 0..117</a>
%F A294988 a(n) ~ 9^(9*n + 3/2) / (16 * Pi^4 * n^4). - _Vaclav Kotesovec_, Sep 20 2019
%p A294988 b:= proc(n, r, p, k) option remember;
%p A294988       `if`(n<r, 0, `if`(r=0, `if`(n=0, p!, 0), add(
%p A294988        b(n-j, k*(r-j), p+j, k)/j!, j=0..min(n, r))))
%p A294988     end:
%p A294988 a:= n-> (k-> `if`(n=0, 1, b(k*n+1, 1, 0, n+1)))(9):
%p A294988 seq(a(n), n=0..10);
%t A294988 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]}]]];
%t A294988 a[n_] := If[n == 0, 1, b[#*n + 1, 1, 0, n + 1]]&[9];
%t A294988 Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, May 21 2018, translated from Maple *)
%Y A294988 Row n=9 of A294746.
%K A294988 nonn
%O A294988 0,2
%A A294988 _Alois P. Heinz_, Nov 12 2017