A243744 - OEIS

%I #7 Feb 10 2015 04:01:06

%S 1,0,0,0,0,0,0,0,0,1,10,55,220,715,2002,5005,11440,24310,48621,92388,

%T 168025,294260,498850,822712,1327029,2107325,3324750,5280276,8595025,

%U 14648920,26637015,52076915,108669142,237787000,535084341,1219016810,2782344676

%N Number of compositions of n with exactly nine occurrences of the largest part.

%H Joerg Arndt and Alois P. Heinz, <a href="/A243744/b243744.txt">Table of n, a(n) for n = 9..650</a>

%p b:= proc(n, p, i) option remember; `if`(n=0, p!,

%p       `if`(i<1, 0, add(b(n-i*j, p+j, i-1)/j!, j=0..n/i)))

%p     end:

%p a:= proc(n) local k; k:=9;

%p       add(b(n-i*k, k, i-1)/k!, i=1..n/k)

%p     end:

%p seq(a(n), n=9..50);

%t b[n_, p_, i_] := b[n, p, i] = If[n == 0, p!, If[i<1, 0, Sum[b[n-i*j, p+j, i-1]/j!, {j, 0, n/i}]]]; a[n_] := (k=9; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 9, 50}] (* _Jean-François Alcover_, Feb 10 2015, after Maple *)

%Y Column k=9 of A238341.

%K nonn

%O 9,11

%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 09 2014