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Search: id:A077335
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| A077335 |
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Sum of products of squares of parts in all partitions of n. |
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+0
1
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| 1, 1, 5, 14, 46, 107, 352, 789, 2314, 5596, 14734, 34572, 92715, 210638, 531342, 1250635, 3042596, 6973974, 16973478, 38399806, 91301956, 207992892, 483244305, 1089029008, 2533640066, 5642905974, 12912848789, 28893132440
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OFFSET
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0,3
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FORMULA
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G.f.: 1/Product_{m>0} (1-m^2*x^m). Recurrence: a(n) = 1/n*Sum_{k=1..n} b(k)*a(n-k), where b(k) = Sum_{d divides k} d^(2*k/d+1).
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EXAMPLE
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The partitions of 4 are 4, 1+3, 2+2, 2+1+1, 1+1+1+1, the corresponding products of squares of parts are 16,9,16,4,1 and their sum is a(4) = 46.
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CROSSREFS
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Cf. A006906, A074141.
Sequence in context: A125246 A140796 A100059 this_sequence A126729 A098730 A163608
Adjacent sequences: A077332 A077333 A077334 this_sequence A077336 A077337 A077338
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)eunet.rs), Nov 30 2002
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