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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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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; refs; listen; history; internal format)
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OFFSET
| 0,3
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COMMENTS
| 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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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..300
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FORMULA
| G.f.: sqrt((5*x^2+2*x-1+(x+1)*sqrt(5*x^2-6*x+1))/(2*x*(1-x)*(5*x+4)*(5*x-1))) - Mark van Hoeij, Nov 16 2011
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MATHEMATICA
| 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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PROG
| (MAGMA) P<x>:=PolynomialRing(Integers()); [n eq 0 select 0 else Coefficients((1+x+x^2+x^3+x^4)^n)[2*n+2]: n in [0..22]]; // Bruno Berselli, Nov 17 2011
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CROSSREFS
| Cf. A035343 (triangle of pentanomial coefficients).
Sequence in context: A037965 A045902 A090017 * A106391 A063881 A181610
Adjacent sequences: A104628 A104629 A104630 * A104632 A104633 A104634
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KEYWORD
| nonn,easy
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AUTHOR
| T. D. Noe (noe(AT)sspectra.com), Mar 17 2005
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