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%I #7 Feb 10 2015 04:00:41
%S 1,0,0,0,0,1,6,21,56,126,253,468,819,1385,2317,3928,6908,12803,25079,
%T 51415,108598,232784,500780,1073700,2285703,4822956,10082161,20884730,
%U 42892750,87405633,176867184,355685658,711460052,1416584340,2809770487,5555833511
%N Number of compositions of n with exactly five occurrences of the largest part.
%H Joerg Arndt and Alois P. Heinz, <a href="/A243740/b243740.txt">Table of n, a(n) for n = 5..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:=5;
%p add(b(n-i*k, k, i-1)/k!, i=1..n/k)
%p end:
%p seq(a(n), n=5..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=5; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 5, 40}] (* _Jean-François Alcover_, Feb 10 2015, after Maple *)
%Y Column k=5 of A238341.
%K nonn
%O 5,7
%A _Joerg Arndt_ and _Alois P. Heinz_, Jun 09 2014
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