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Search: id:A005716
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| A005716 |
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Coefficient of x^8 in expansion of (1+x+x^2)^n
(Formerly M4975)
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+0
9
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| 1, 15, 90, 357, 1107, 2907, 6765, 14355, 28314, 52624, 93093, 157950, 258570, 410346, 633726, 955434, 1409895, 2040885, 2903428, 4065963, 5612805, 7646925, 10293075, 13701285, 18050760, 23554206, 30462615, 39070540, 49721892
(list; graph; listen)
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OFFSET
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4,2
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COMMENT
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a(n) = A111808(n,8) for n>7. - Reinhard Zumkeller (reinhard.zumkeller(AT)lhsystems.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+1, 5)*(n^2+23*n-84)*(n+10)/336, n >= 4.
G.f.: (x^4)*(1+6*x-9*x^2+3*x^3)/(1-x)^9 (Numerator polynomial is N3(8, x) from A063420.)
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MAPLE
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A005716:=-(6*z-9*z**2+3*z**3+1)/(z-1)**9; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Cf. A000574, A005581, A005712, A005714, A005715.
a(n)= A027907(n, 8), n >= 4 (ninth column of trinomial coefficients).
Sequence in context: A010822 A022707 A001297 this_sequence A048630 A035163 A020242
Adjacent sequences: A005713 A005714 A005715 this_sequence A005717 A005718 A005719
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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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