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Number of compositions of n with exactly seven occurrences of the largest part.
2

%I #7 Feb 10 2015 04:00:54

%S 1,0,0,0,0,0,0,1,8,36,120,330,792,1716,3433,6443,11484,19640,32550,

%T 52860,85296,139249,235001,418473,795544,1610418,3421514,7489962,

%U 16625389,37003313,82024320,180421399,393126594,848051064,1811227670,3831269241,8030748161

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

%H Joerg Arndt and Alois P. Heinz, <a href="/A243742/b243742.txt">Table of n, a(n) for n = 7..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:=7;

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

%p end:

%p seq(a(n), n=7..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=7; Sum[b[n-i*k, k, i-1]/k!, {i, 1, n/k}]); Table[a[n], {n, 7, 40}] (* _Jean-François Alcover_, Feb 10 2015, after Maple *)

%Y Column k=7 of A238341.

%K nonn

%O 7,9

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