login
Number of compositions of n into exactly seven different parts with distinct multiplicities.
2

%I #7 Feb 11 2015 04:10:44

%S 2431106898187968000,25830510793247160000,121150160426367072000,

%T 478913588068635720000,1848522650426852400000,6067325851827648408000,

%U 19158973516499432616000,59882095876893754464000,173801554657753702680000,487295849448575903736000

%N Number of compositions of n into exactly seven different parts with distinct multiplicities.

%H Alois P. Heinz, <a href="/A246234/b246234.txt">Table of n, a(n) for n = 84..120</a>

%t $RecursionLimit = 1000; b[n_, i_, s_List] := b[n, i, s] = If[n == 0, Total[s]!, If[i < 1, 0, Expand[ Sum[ If[j > 0 && MemberQ[s, j], 0, If[j == 0, 1, x]*b[n - i*j, i - 1, If[j == 0, s, s ~Union~ {j}]]/j!], {j, 0, n/i}]]]]; a[n_] := Coefficient[b[n, n, {}], x, 7]; Table[a[n], {n, 84, 100}] (* _Jean-François Alcover_, Feb 11 2015, after _Alois P. Heinz_ *)

%Y Column k=7 of A242896.

%K nonn

%O 84,1

%A _Alois P. Heinz_, Aug 19 2014