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A102434
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Sum_{k=1..n} {number of partitions of n into powers k^m where 0<=m<n}.
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5
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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
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1,2
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COMMENTS
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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).
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LINKS
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Alois P. Heinz, Table of n, a(n) for n = 1..500
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FORMULA
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a(n) = A102433(n) - n + 1 = A102431(n) + C(2n-1,n).
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EXAMPLE
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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
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CROSSREFS
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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
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KEYWORD
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easy,nonn
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AUTHOR
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Marc LeBrun, Jan 08 2005
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EXTENSIONS
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Edited and verified by Franklin T. Adams-Watters, Mar 10, 2006
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STATUS
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approved
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