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%I #10 Sep 20 2019 05:07:09
%S 1,441675,663134389930,2594884910993019575,16336038155342083651640376,
%T 130958058407369286623026190867082,
%U 1206534243283932582765850205674424343577,12176825528022093702548525617184407475359333407,131223281654667714701311635640432890136981994039662720
%N Number of compositions (ordered partitions) of 1 into exactly 8n+1 powers of 1/(n+1).
%H Alois P. Heinz, <a href="/A294987/b294987.txt">Table of n, a(n) for n = 0..139</a>
%F a(n) ~ 8^(8*n + 3/2) / (2*Pi*n)^(7/2). - _Vaclav Kotesovec_, Sep 20 2019
%p b:= proc(n, r, p, k) option remember;
%p `if`(n<r, 0, `if`(r=0, `if`(n=0, p!, 0), add(
%p b(n-j, k*(r-j), p+j, k)/j!, j=0..min(n, r))))
%p end:
%p a:= n-> (k-> `if`(n=0, 1, b(k*n+1, 1, 0, n+1)))(8):
%p seq(a(n), n=0..12);
%t 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 a[n_] := If[n == 0, 1, b[#*n + 1, 1, 0, n + 1]]&[8];
%t Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, May 21 2018, translated from Maple *)
%Y Row n=8 of A294746.
%K nonn
%O 0,2
%A _Alois P. Heinz_, Nov 12 2017