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%I #6 Jun 24 2014 01:10:00
%S 1,1,2,2,3,2,4,3,5,5,7,8,10,8,13,14,15,18,20,23,29,31,36,41,49,54,63,
%T 72,80,92,108,116,137,153,174,197,222,250,281,318,354,398,450,497,561,
%U 624,697,779,869,964,1075,1193,1325,1471,1635,1809,2004,2217,2455,2711
%N a(n) = number of solutions to x_1 + x_2 + ... + x_n = x_{n+1} where each x_i is a factorial.
%e a[6]=3 since 5!+5!+5!+5!+5!+5!=6!, 3!+3!+3!+2!+2!+2!=4! and 1!+1!+1!+1!+1!+1!=3!
%t f[n_, k_, m_] := (* # of partitions of n into k factorials <= m! *) Which[n==k, 1, m<=1||n<k|| n>k m!, 0, True, f[n, k, m]=f[n, k, m-1]+f[n-m!, k-1, m]]; a[n_] := Sum[f[r!, n, r-1], {r, 2, n}];
%K nonn
%O 2,3
%A _Erich Friedman_, Jun 23 2001
%E More terms from _Dean Hickerson_, Jun 25, 2001
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