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A002419
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4-dimensional figurate numbers: (6n-2)*C(n+2,3)/4.
(Formerly M4699 N2008)
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8
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1, 10, 40, 110, 245, 476, 840, 1380, 2145, 3190, 4576, 6370, 8645, 11480, 14960, 19176, 24225, 30210, 37240, 45430, 54901, 65780, 78200, 92300, 108225, 126126, 146160, 168490, 193285, 220720, 250976, 284240, 320705, 360570, 404040, 451326
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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REFERENCES
| A. H. Beiler, Recreations in the Theory of Numbers, Dover, NY, 1964, p. 195.
N. J. A. Sloane, A Handbook of Integer Sequences, Academic Press, 1973 (includes this sequence).
N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).
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LINKS
| 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.
Index to sequences with linear recurrences with constant coefficients, signature (5,-10,10,-5,1)
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FORMULA
| a(n)= (3*n-1)*binomial(n+2, 3)/2, n>=1. G.f.: x*(1+5*x)/(1-x)^5.
sum{n>=1} 1/a(n) = (-24+81*log(3) -9*Pi*sqrt(3))/14 = 1.143929... - R. J. Mathar, Mar 29 2011
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MAPLE
| A002419:=-(1+5*z)/(z-1)**5; [S. Plouffe in his 1992 dissertation.]
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CROSSREFS
| Cf. A093563 ((6, 1) Pascal, column m=4). A002414 (differences).
Sequence in context: A131037 A071233 A063490 * A199826 A027981 A013977
Adjacent sequences: A002416 A002417 A002418 * A002420 A002421 A002422
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KEYWORD
| nonn,easy
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| More terms from Pab Ter (pabrlos(AT)yahoo.com), May 08 2004
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