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A162506
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Convergent of an infinite product, a*b*c,...; a = [1,1,1,...], b = [1,0,2,0,2,0,2,...], c = [1,0,0,3,0,0,3,0,0,3,...],...
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3
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1, 1, 3, 6, 12, 23, 42, 77, 132, 236, 390, 664, 1087, 1782, 2858, 4601, 7216, 11344, 17650, 27162, 41632, 63316, 95717, 143558, 214644, 318464, 470879, 691968, 1012866, 1474434, 2140606, 3088874, 4445440, 6370142, 9095564, 12941289
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,3
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COMMENTS
| Equals row sums of triangle A162507.
Sum of products of parts, counted without multiplicity, in all partitions of n. Sum of products of parts, counted with multiplicity, in all partitions of n is A006906. [From Vladeta Jovovic (vladeta(AT)eunet.yu), Jul 24 2009]
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FORMULA
| Convergent of an infinite product, a*b*c,...; a = [1,1,1,...], b =
[1,0,2,0,2,0,2,...], c = [1,0,0,3,0,0,3,0,0,3,...]; i.e. the infinite set of
sequences [1,...N,...,] interleaved with (N-2) adjacent zeros.
G.f.: Product(1+k*x^k/(1-x^k),k=1..infinity). [From Vladeta Jovovic (vladeta(AT)eunet.yu), Jul 24 2009]
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EXAMPLE
| First few rows of the array =
1,...1,...1,...1,...1,...
1,...1,...3,...3,...5,...
1,...1,...3,...6,...8,...
1,...1,...3,...6,..12,...
1,...1,...3,...6,..12,...
...tending to A162506: (1, 1, 3, 6, 12, 23, 42, 77, 132,...)
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CROSSREFS
| A162507
Sequence in context: A097939 A174201 A181844 * A055244 A089068 A018180
Adjacent sequences: A162503 A162504 A162505 * A162507 A162508 A162509
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 04 2009
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EXTENSIONS
| More terms from Vladeta Jovovic (vladeta(AT)eunet.yu), Jul 22 2009
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