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A117485
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G.f.: 1/((1-x)*(1-x^2)*(1-x^3))^2.
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6
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1, 2, 5, 10, 18, 30, 49, 74, 110, 158, 221, 302, 407, 536, 698, 896, 1136, 1424, 1770, 2176, 2656, 3216, 3866, 4616, 5481, 6466, 7591, 8866, 10306, 11926, 13747, 15778, 18046, 20566, 23359, 26446, 29855, 33600, 37716, 42224, 47152, 52528, 58388, 64752, 71664
(list; graph; refs; listen; history; internal format)
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OFFSET
| 9,2
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COMMENTS
| Molien series for S_3 X S_3, cf. A001399.
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EXAMPLE
| As a cross-check, row sixteen of A115994 yields p(16) = 16 + 140 + 74 + 1.
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MAPLE
| with(combstruct):ZL:=[st, {st=Prod(left, right), left=Set(U, card=r), right=Set(U, card=r), U=Sequence(Z, card>=1)}, unlabeled]: subs(r=3, stack): seq(count(subs(r=3, ZL), size=m), m=6..50) ; - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 02 2008
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MATHEMATICA
| CoefficientList[Series[1/((1-x)(1-x^2)(1-x^3))^2, {x, 0, 50}], x] (* From Harvey P. Dale, Oct 09 2011 *)
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PROG
| (MAGMA) n:=3; G:=SymmetricGroup(n); H:=DirectProduct(G, G); MolienSeries(H); [N. J. A. Sloane]
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CROSSREFS
| Column one of A115994 is A000027 and column two is A006918 beginning at row four; column three begins at row nine with the present sequence.
Cf. A000027, A006918, A117488, A117489, A001399, A117486.
Sequence in context: A025223 A177787 A104688 * A084835 A034350 A006327
Adjacent sequences: A117482 A117483 A117484 * A117486 A117487 A117488
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KEYWORD
| nonn
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AUTHOR
| Alford Arnold (Alford1940(AT)aol.com), Mar 22 2006
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EXTENSIONS
| Entry revised by N. J. A. Sloane (njas(AT)research.att.com), Mar 10 2007
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