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Search: id:A117487
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| A117487 |
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G.f.: 1/((1-x)*(1-x^2)*(1-x^3)*(1-x^4)*(1-x^5))^2. |
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+0
2
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| 1, 2, 5, 10, 20, 36, 63, 104, 169, 264, 405, 604, 888, 1278, 1815, 2536, 3502, 4772, 6437, 8586, 11352, 14866, 19315, 24890, 31851, 40466, 51089, 64092, 79952, 99172, 122386, 150264, 183639, 223394, 270605, 326422, 392225, 469490, 559970, 665542, 788412
(list; graph; listen)
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OFFSET
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1,2
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COMMENT
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Molien series for S_5 X S_5, cf. A001401.
Molien series for S_k X S_k approaches A000712 as k increases.
Column 5 of table A115994. A115994 is a triangle read by rows: T(n,k) is number of partitions of n with Durfee square of size k; at row 25 there is only one partition having a Durfee square of size five, so a(1) = 1.
Note that a(5) is 20, the scalar product of (1 1 2 3 5) and (5 3 2 1 1 ). a(6) is 36, the scalar product of (1 1 2 3 5 7) and (7 5 3 2 1 1 ).
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MAPLE
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# adapted from A115994 kmax := 120 : qmax := kmax/2 : g:=sum(t^k*q^(k^2)/product((1-q^j)^2, j=1..k), k=1..kmax): gser:=series(g, q=0, qmax): for n from 25 to qmax-1 do P :=coeff(gser, q^n) : printf("%a, ", coeff(P, t^5)); od: - R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2006
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PROGRAM
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(MAGMA) n:=5; G:=SymmetricGroup(n); H:=DirectProduct(G, G); MolienSeries(H); [njas]
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CROSSREFS
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Cf. A001400, A001399, A117485, A117486, A117488, A117489.
Cf. A000027, A006918, A115994, A000712.
Sequence in context: A126105 A117486 A000710 this_sequence A103924 A103925 A103926
Adjacent sequences: A117484 A117485 A117486 this_sequence A117488 A117489 A117490
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KEYWORD
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nonn
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AUTHOR
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Alford Arnold (Alford1940(AT)aol.com), Mar 22 2006
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EXTENSIONS
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More terms from R. J. Mathar (mathar(AT)strw.leidenuniv.nl), Apr 07 2006
Entry revised by njas, Mar 10 2007
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