

A102434


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


5



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

1,2


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(2n1,n).


LINKS

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


FORMULA

a(n) = A102433(n)  n + 1 = A102431(n) + C(2n1,n).


EXAMPLE

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


CROSSREFS

Cf. A001700, A102430, A102431, A102432, A102433, A018819, A062051.
Sequence in context: A210972 A197607 A296829 * A186649 A120901 A222988
Adjacent sequences: A102431 A102432 A102433 * A102435 A102436 A102437


KEYWORD

easy,nonn


AUTHOR

Marc LeBrun, Jan 08 2005


EXTENSIONS

Edited and verified by Franklin T. AdamsWatters, Mar 10, 2006


STATUS

approved



