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%I #8 Mar 31 2012 13:21:29
%S 1,5,14,43,136,477,1733,6459,24338,92413,352753,1352127,5200351,
%T 20058360,77558825,300540275,1166803192,4537567749,17672632001,
%U 68923264531,269128937347,1052049482004,4116715363946,16123801841726
%N Sum_{k=1..n} {number of partitions of n into powers k^m where 0<=m<n}.
%C Equivalently, Sum_{k=2}^n (Number of partitions of n into powers of k) + Number of partitions of n into n 1's; the latter term is C(2n-1,n).
%H Alois P. Heinz, <a href="/A102434/b102434.txt">Table of n, a(n) for n = 1..500</a>
%F a(n) = A102433(n) - n + 1 = A102431(n) + C(2n-1,n).
%e a(2) = 5; 3 partitions for k=1: 2.1^0, 1.1^1+1.1^0, 2.1^1; and 2 for k=2: 2.2^0, 1.2^1
%Y Cf. A001700, A102430, A102431, A102432, A102433, A018819, A062051.
%K easy,nonn
%O 1,2
%A _Marc LeBrun_, Jan 08 2005
%E Edited and verified by _Franklin T. Adams-Watters_, Mar 10, 2006
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