A294986 - OEIS

%I #10 Sep 20 2019 05:06:41

%S 1,41245,4561368175,1104353764428365,396695587555058190126,

%T 174436242482643190451211853,86237678200608256132213084584295,

%U 46050764886573707269872023694736134925,25997337847684377365651388718120083246723460

%N Number of compositions (ordered partitions) of 1 into exactly 7n+1 powers of 1/(n+1).

%H Alois P. Heinz, <a href="/A294986/b294986.txt">Table of n, a(n) for n = 0..170</a>

%F a(n) ~ 7^(7*n + 3/2) / (8 * Pi^3 * n^3). - _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)))(7):

%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]]&[7];

%t Table[a[n], {n, 0, 12}] (* _Jean-François Alcover_, May 21 2018, translated from Maple *)

%Y Row n=7 of A294746.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Nov 12 2017