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A004987
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(3^n/n!)*product[ k=0..n-1 ](3*k + 1).
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5
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1, 3, 18, 126, 945, 7371, 58968, 480168, 3961386, 33011550, 277297020, 2344420260, 19927572210, 170150808870, 1458435504600, 12542545339560, 108179453553705, 935434098376155, 8107095519260010, 70403724246205350
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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LINKS
| A. Straub, V. H. Moll, T. Amdeberhan, The p-adic valuation of k-central binomial coefficients, Acta Arith. 140 (2009) 31-41, eq (1.10)
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FORMULA
| G.f.: (1 - 9*x)^(-1/3). a(n)=(3^n/n!)*A007559(n), n >= 1, a(0) := 1.
a(n) ~ Gamma(1/3)^-1*n^(-2/3)*3^(2*n)*{1 - 1/9*n^-1 + ...}.
Representation as n-th moment of a positive function on (0, 9): a(n)=int(x^n*(1/(Pi*sqrt(3)*6*(x/9)^(2/3)*(1-x/9)^(1/3))), x=0..9), n=0, 1... .This function is the solution of the Hausdorff moment problem on (0, 9) with moments equal to a(n). As a consequence this representation is unique. - Karol A. Penson (penson(AT)lptl.jussieu.fr), Jan 30, 2003.
G.f. : (1-9x)^(-1/3) - Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 05 2004
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CROSSREFS
| Cf. A004117, A007559, A047657, A054861, A034689, A053101, A072888.
Sequence in context: A108241 A199421 A176277 * A074557 A073971 A120922
Adjacent sequences: A004984 A004985 A004986 * A004988 A004989 A004990
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KEYWORD
| nonn
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AUTHOR
| Joe Keane (jgk(AT)jgk.org)
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EXTENSIONS
| More terms from R. Stephan, Mar 13 2004
More terms from Benoit Cloitre (benoit7848c(AT)orange.fr), Jun 05 2004
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