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A118266
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Coefficient of q^n in (1-q)^5/(1-5q); dimensions of the enveloping algebra of the derived free Lie algebra on 5 letters.
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3
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1, 0, 10, 40, 205, 1024, 5120, 25600, 128000, 640000, 3200000, 16000000, 80000000, 400000000, 2000000000, 10000000000, 50000000000, 250000000000, 1250000000000, 6250000000000, 31250000000000, 156250000000000
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| For n>=5, a(n) is equal to the number of functions f:{1,2,...,n}->{1,2,3,4,5} such that for fixed, different x_1, x_2, x_3, x_4, x_5 in {1,2,...,n} and fixed y_1, y_2, y_3, y_ 4, y_5 in {1,2,3,4,5} we have f(x_i)<>y_i, (i=1,2,3,4,5). - Milan R. Janjic (agnus(AT)blic.net), May 13 2007
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REFERENCES
| N. Bergeron, C. Reutenauer, M. Rosas, M. Zabrocki, Invariants and Coinvariants of the Symmetric Group in Noncommuting Variables, http://arXiv.org/abs/math.CO/0502082, to appear Canad. Math J.
C. Reutenauer, Free Lie algebras. London Mathematical Society Monographs. New Series, 7. Oxford Science Publications. The Clarendon Press, Oxford University Press, New York, 1993. xviii+269 pp.
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LINKS
| Milan Janjic, Enumerative Formulas for Some Functions on Finite Sets
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FORMULA
| g.f. (1-q)^5/(1-5q) sum( (-1)^k*C(5,k) 5^(n-k); k=0..min(n,5));
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MAPLE
| f:=n->add((-1)^k*C(5, k)*5^(n-k), k=0..min(n, 4)); seq(f(i), i=0..15);
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CROSSREFS
| Cf. A001692, A118264, A118265.
Sequence in context: A002066 A061991 A060580 * A054885 A000449 A027274
Adjacent sequences: A118263 A118264 A118265 * A118267 A118268 A118269
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KEYWORD
| nonn
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AUTHOR
| Mike Zabrocki (zabrocki(AT)mathstat.yorku.ca), Apr 20 2006
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