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Search: id:A001919
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| A001919 |
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Eighth column of quadrinomial coefficients.
(Formerly M4234 N1769)
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+0
2
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| 6, 40, 155, 456, 1128, 2472, 4950, 9240, 16302, 27456, 44473, 69680, 106080, 157488, 228684, 325584, 455430, 627000, 850839, 1139512, 1507880, 1973400, 2556450, 3280680, 4173390, 5265936, 6594165, 8198880, 10126336, 12428768, 15164952
(list; graph; listen)
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OFFSET
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3,1
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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).
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
L. Carlitz et al., Permutations and sequences with repetions by number of increases, J. Combin. Theory, 1 (1966), 350-374.
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.
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FORMULA
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a(n)= A008287(n, 7)= binomial(n+2, 5)*(n^2+21*n+180 )/42, n >= 3.
G.f.: (x^3)*(6-8*x+3*x^2 )/(1-x)^8. Numerator polynomial is N4(7, x) from array A063421.
a(n)=n(n^2-1)(n^2-4)(n^2+21n+180)/5040 - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 27 2005
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MAPLE
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seq(n*(n^2-1)*(n^2-4)*(n^2+21*n+180)/5040, n=3..34); (Deutsch)
A001919:=(3*z**2-8*z+6)/(z-1)**8; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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Adjacent sequences: A001916 A001917 A001918 this_sequence A001920 A001921 A001922
Sequence in context: A089207 A027777 A073773 this_sequence A005553 A055344 A059021
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KEYWORD
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nonn,easy
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AUTHOR
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N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
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More terms from Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 27 2005
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