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Search: id:A005715
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| A005715 |
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Coefficient of x^7 in expansion of (1+x+x^2)^n.
(Formerly M3632)
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+0
5
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| 4, 30, 126, 393, 1016, 2304, 4740, 9042, 16236, 27742, 45474, 71955, 110448, 165104, 241128, 344964, 484500, 669294, 910822, 1222749, 1621224, 2125200, 2756780, 3541590, 4509180, 5693454, 7133130, 8872231, 10960608, 13454496
(list; graph; listen)
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OFFSET
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4,1
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COMMENT
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a(n) = A111808(n,7) for n>6. - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Aug 17 2005
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REFERENCES
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
L. Comtet, Advanced Combinatorics, Reidel, 1974, p. 78.
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LINKS
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S. Plouffe, Approximations de S\'{e}ries G\'{e}n\'{e}ratrices et Quelques Conjectures}, Dissertation, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
S. Plouffe, 1031 Generating Functions and Conjectures, Universit\'{e} du Qu\'{e}bec \`{a} Montr\'{e}al, 1992.
Eric Weisstein's World of Mathematics, Trinomial Coefficient
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FORMULA
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a(n)=binomial(n, 4)*(n^3+27*n^2+116*n-120)/210, n >= 4.
G.f.: (x^4)*(x-2)*(x^2-2)/(1-x)^8 (Numerator polynomial is N3(7, x) from A063420.)
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MAPLE
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A005715:=(z-2)*(z**2-2)/(z-1)**8; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A000574, A005581, A005712, A005714, A005716.
a(n)= A027907(n, 7), n >= 4 (eighth column of trinomial coefficients).
Adjacent sequences: A005712 A005713 A005714 this_sequence A005716 A005717 A005718
Sequence in context: A027445 A027789 A130424 this_sequence A123351 A119697 A132849
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KEYWORD
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nonn
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AUTHOR
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njas
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Oct 02 2000
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