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Search: id:A092485
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| A092485 |
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Expansion of Product_{m=1..inf} (1+m*(m+1)*q^m). |
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1
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| 1, 2, 6, 24, 44, 142, 366, 800, 1636, 4338, 10154, 18968, 42368, 80726, 183914, 401096, 729944, 1402098, 2829814, 5172416, 10600836, 21582558, 37732782, 70148512, 127184636, 236798322, 416265730, 804045376, 1514022088, 2581172630
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OFFSET
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0,2
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COMMENT
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Sum of product of i(i+1)-transform of terms in all partitions of n into distinct parts.
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EXAMPLE
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The partitions of 6 into distinct parts are 6, 1+5, 2+4, 1+2+3, the corresponding i(i+1)-transforms are of products 6.7, 2.5.6, 2.3.4.5, 2.2.3.3.4, so 42, 60, 120, 144 and their sum is a(6) = 366.
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MATHEMATICA
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Take[ CoefficientList[ Expand[ Product[1 + m(m + 1)q^m, {m, 1000}]], q], 30] - Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 05 2004
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CROSSREFS
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Cf. A022629.
Sequence in context: A067653 A090755 A004306 this_sequence A113904 A099144 A104114
Adjacent sequences: A092482 A092483 A092484 this_sequence A092486 A092487 A092488
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KEYWORD
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nonn
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AUTHOR
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Jon Perry (perry(AT)globalnet.co.uk), Apr 04 2004
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EXTENSIONS
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More terms from Robert G. Wilson v (rgwv(AT)rgwv.com), Apr 05 2004
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