A102434 Sum_{k=1..n} {number of partitions of n into powers k^m where 0<=m

1, 5, 14, 43, 136, 477, 1733, 6459, 24338, 92413, 352753, 1352127, 5200351, 20058360, 77558825, 300540275, 1166803192, 4537567749, 17672632001, 68923264531, 269128937347, 1052049482004, 4116715363946, 16123801841726

Offset: 1

Author

Marc LeBrun, Jan 08 2005

Keywords

• easy
• nonn

Comments

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).

Examples

			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
		

Links

• Alois P. Heinz, Table of n, a(n) for n = 1..500

Crossrefs

Cf. A001700, A102430, A102431, A102432, A102433, A018819, A062051.

Formula

a(n) = A102433(n) - n + 1 = A102431(n) + C(2n-1,n).

Extensions

Edited and verified by Franklin T. Adams-Watters, Mar 10 2006