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Search: id:A104631
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| A104631 |
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Coefficient of x^(2n+1) in the expansion of (1+x+x^2+x^3+x^4)^n. |
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+0
2
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| 0, 1, 4, 18, 80, 365, 1686, 7875, 37080, 175725, 837100, 4004770, 19227924, 92599533, 447118140, 2163837030, 10492874384, 50972030189, 248000853348, 1208335275170, 5894873067200, 28791371852145, 140768761906190
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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In the triangle of pentanomial coefficients, these numbers are in the column next to the central pentanomial coefficients, A005191. Note that for n>0, n divides a(n). This divisibility property is also true for the triangle of trinomial coefficients, A027907, but apparently for no other triangle of m-nomial coefficients. The quotient a(n)/n is in A104632.
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MATHEMATICA
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f=1; Table[f=Expand[f(x^4+x^3+x^2+x+1)]; Coefficient[f, x, 2n+1], {n, 30}]
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CROSSREFS
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Cf. A035343 (triangle of pentanomial coefficients).
Sequence in context: A037965 A045902 A090017 this_sequence A106391 A063881 A100192
Adjacent sequences: A104628 A104629 A104630 this_sequence A104632 A104633 A104634
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KEYWORD
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easy,nonn
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AUTHOR
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T. D. Noe (noe(AT)sspectra.com), Mar 17 2005
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