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A025148
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Number of partitions of n into distinct parts >= 3.
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5
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1, 0, 0, 1, 1, 1, 1, 2, 2, 3, 3, 4, 5, 6, 7, 9, 10, 12, 15, 17, 20, 24, 28, 32, 38, 44, 51, 59, 68, 78, 91, 103, 118, 136, 155, 176, 201, 228, 259, 294, 332, 375, 425, 478, 538, 607, 681, 764, 858, 961, 1075, 1203, 1343, 1499, 1673, 1863, 2073, 2308, 2564, 2847, 3161, 3504
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,8
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FORMULA
| G.f.: Product_{k=3..inf} (1+x^k).
a(n)=A096749(n+2). - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Jul 31 2008
G.f.: sum(n>=0, x^(n*(n+5)/2) / prod(k=1..n, 1-x^k) ); special case of g.f. for partitions into distinct parts >= L, sum(n>=0, x^(n*(n+2*L-1)/2) / prod(k=1..n, 1-x^k) ). [Joerg Arndt, Mar 24 2011]
G.f.: sum(n>=2, x^(n*(n+1)/2-3) / prod(k=1..n-2, 1-x^k) ), a special case of the g.f. for partitions into distinct parts >= L, sum(n>=L-1, x^(n*(n+1)/2-L*(L-1)/2) / prod(k=1..n-(L-1), 1-x^k) ). [Joerg Arndt, Mar 27 2011]
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MAPLE
| with(combstruct) ; sys := {L = PowerSet(Sequence(Z, card>2)) }; seq( count([L, sys], size=i), i=0..56 ); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Mar 08 2007
A025148 := proc(n) mul(1+x^k, k=3..n+1) ; expand(%) ; coeftayl(%, x=0, n) ; end proc: # R. J. Mathar, Mar 28 2011
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CROSSREFS
| Cf. A025147.
Sequence in context: A185227 A026823 * A096749 A036821 A026798 A185325
Adjacent sequences: A025145 A025146 A025147 * A025149 A025150 A025151
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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