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Search: id:A005720
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| A005720 |
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Quadrinomial coefficients.
(Formerly M4702)
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+0
1
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| 1, 10, 44, 135, 336, 728, 1428, 2598, 4455, 7282, 11440, 17381, 25662, 36960, 52088, 72012, 97869, 130986, 172900, 225379, 290444, 370392, 467820, 585650, 727155, 895986, 1096200, 1332289, 1609210, 1932416, 2307888, 2742168, 3242393, 3816330, 4472412, 5219775
(list; graph; listen)
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OFFSET
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2,2
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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.
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FORMULA
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a(n)= binomial(n+1, 3)*(n^3+15*n^2+86*n-120)/120, n >= 2.
G.f.: (x^2)*(1+3*x-5*x^2+2*x^3)/(1-x)^7 (numerator polynomial is N4(6, x) from A063421.)
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MAPLE
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A005720:=-(1+3*z-5*z**2+2*z**3)/(z-1)**7; [Conjectured by S. Plouffe in his 1992 dissertation.]
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CROSSREFS
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a(n)= A008287(n, 6), n >= 2 (seventh column of quadrinomial coefficients).
Adjacent sequences: A005717 A005718 A005719 this_sequence A005721 A005722 A005723
Sequence in context: A008532 A085582 A058310 this_sequence A060326 A124852 A097416
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KEYWORD
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nonn
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AUTHOR
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njas
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