A294989 - OEIS

%I #10 Sep 20 2019 05:08:00

%S 1,68958747,27212315953140892,39880061006390454401626995,

%T 110656003660578876500875377620844376,

%U 423205992807070499591372608204571223421862945,1944053748730350081768848916806347783770184147756976500

%N Number of compositions (ordered partitions) of 1 into exactly 10n+1 powers of 1/(n+1).

%H Alois P. Heinz, <a href="/A294989/b294989.txt">Table of n, a(n) for n = 0..101</a>

%F a(n) ~ 10^(10*n + 3/2) / (2*Pi*n)^(9/2). - _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)))(10):

%p seq(a(n), n=0..10);

%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]]&[10];

%t Table[a[n], {n, 0, 10}] (* _Jean-François Alcover_, May 21 2018, translated from Maple *)

%Y Row n=10 of A294746.

%K nonn

%O 0,2

%A _Alois P. Heinz_, Nov 12 2017