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Search: id:A006846
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| A006846 |
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Hammersley's polynomial p_n(1).
(Formerly M1807)
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+0
9
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| 1, 1, 2, 7, 41, 376, 5033, 92821, 2257166, 69981919, 2694447797, 126128146156, 7054258103921, 464584757637001, 35586641825705882, 3136942184333040727
(list; graph; listen)
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OFFSET
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0,3
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COMMENT
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Equals column 0 of triangle A104027. Also equals column 0 of triangle A104030 (offset 1). Both A104027 and A104030 involve the trinomial coefficients. - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 06 2005
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REFERENCES
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N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
J. M. Hammersley, An undergraduate exercise in manipulation, Math. Scientist, 14 (1989), 1-23.
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FORMULA
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a(n) = sum_{k>=0} (-1)^(n+k)*A065547(n, k) = sum_{k>=0} A085707(n, k) . - DELEHAM Philippe (kolotoko(AT)wanadoo.fr), Feb 26 2004
E.g.f.: cosh(sqrt(3)*x/2)/cos(x/2) = Sum_{n>=0} a(n)*x^(2n)/(2n)!. - Paul D. Hanna (pauldhanna(AT)juno.com), Feb 27 2005
a(n) = (-1)^n*A104027(n, 0). a(n+1) = (-1)^(n+1)*A104030(n, 0). - Paul D. Hanna (pauldhanna(AT)juno.com), Mar 06 2005
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MAPLE
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{a(n)=local(X=x+x*O(x^(2*n))); round((2*n)!*polcoeff(cosh(sqrt(3)*X/2)/cos(X/2), 2*n))} (Hanna)
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CROSSREFS
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Cf. A104027, A104030.
Sequence in context: A006677 A101390 A113144 this_sequence A047864 A163921 A008934
Adjacent sequences: A006843 A006844 A006845 this_sequence A006847 A006848 A006849
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KEYWORD
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nonn
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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