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Search: id:A098504
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| A098504 |
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Number of compositions of n such that every part occurs with the same multiplicity. |
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+0
2
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| 1, 2, 4, 5, 6, 20, 14, 28, 49, 72, 66, 298, 134, 304, 646, 707, 618, 3794, 1178, 4856, 7926, 6300, 4758, 64004, 9267, 19624, 69346, 76148, 30462, 1491780, 55742, 294642, 1181578, 386820, 932804, 21400221, 315974, 1045372, 12081290, 66532116, 958265
(list; graph; listen)
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OFFSET
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1,2
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FORMULA
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G.f.: Sum(Sum((l*k)!/l!^k*x^(l*k*(k+1)/2)/Product(1-x^(l*j), j=1..k), k=1..infinity), l=1..infinity).
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EXAMPLE
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a(6)=20 because we have 6, 15, 51, 24, 42, 33, 123, 132, 213, 231, 312, 321, 222, 1122, 1212, 1221, 2112, 2121, 2211, and 111111.
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MAPLE
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G:=sum(sum((l*k)!/l!^k*x^(l*k*(k+1)/2)/product(1-x^(l*j), j=1..k), k=1..40), l=1..55):Gser:=series(G, x=0, 55):seq(coeff(Gser, x^n), n=1..46); (Deutsch)
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CROSSREFS
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Cf. A047966, A032020.
Adjacent sequences: A098501 A098502 A098503 this_sequence A098505 A098506 A098507
Sequence in context: A026473 A008319 A033311 this_sequence A137653 A021411 A005532
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KEYWORD
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nonn
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AUTHOR
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Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 26 2004
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Mar 28 2005
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