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Search: id:A076657
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| A076657 |
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a(n)=(1/24) * binom(2n,n)(16^n-binom(2n,n)^2). Right side of identity involving series A005148. |
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+0
1
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| 0, 1, 55, 3080, 176855, 10343256, 613052440, 36701926976, 2214353424855, 134425330290680, 8201448540559560, 502460159228920256, 30890758976011469080, 1904794982716556862400, 117756015163729064222400
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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The members of the sequence have exceptionally many small prime factors.
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REFERENCES
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D. Shanks, Solved and unsolved problems in number theory, Chelsea NY, 1985, pp. 256-257 (F. Beukers, Letter to D. Shanks, Mar. 13, 1984).
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FORMULA
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a(n) = (1/24) * binom(2n, n)(16^n-binom(2n, n)^2) = sum_i^n binom(2n-2i, n-i)^3 A005148(n) (Shanks and Beukers)
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MATHEMATICA
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a[n_] := (Binomial[2n, n]*(16^n-Binomial[2n, n]^2))/24
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PROGRAM
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(PARI) a(n)=if(n<0, 0, (binomial(2*n, n)*(16^n-binomial(2*n, n)^2))/24)
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CROSSREFS
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Cf. A005148.
Sequence in context: A131557 A119166 A027548 this_sequence A095659 A081993 A060077
Adjacent sequences: A076654 A076655 A076656 this_sequence A076658 A076659 A076660
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KEYWORD
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nonn
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AUTHOR
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Ralf Stephan (ralf(AT)ark.in-berlin.de), Oct 24 2002
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