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0, 0, 1, 12, 54, 160, 375, 756, 1372, 2304, 3645, 5500, 7986, 11232, 15379, 20580, 27000, 34816, 44217, 55404, 68590, 84000, 101871, 122452, 146004, 172800, 203125, 237276, 275562, 318304, 365835
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,4
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COMMENTS
| a(n)=n(n-1)^3/2 is half the number of colorings of 4 points on a line with n colors. - R. H. Hardin (rhhardin(AT)att.net), Feb 23 2002
n^2*n(n+1)/2: a(n+1) = product of n-th triangular number and n-th square number. E.g. a(4)=6*9=54 - Alexandre Wajnberg (alexandre.wajnberg(AT)skynet.be), Dec 18 2005
a(n)=A000290*A000217 - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 20 2007
A019582[n+2]=denom(2/((n+2)*(n+1)^3)) [From Stephen Crowley (crow(AT)crowlogic.net), Jun 28 2009]
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LINKS
| Vincenzo Librandi, Table of n, a(n) for n = 0..680
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FORMULA
| a(n+1)=sum{k=0..n, n^2(n-k) }=n^3(n+1)/2 - Paul Barry (pbarry(AT)wit.ie), Sep 02 2003
sum(1/A019582[j],j=2..infinity)=hypergeom([1, 1, 1, 1], [2, 2, 3], 1)=2-2*Zeta(2)+2*Zeta(3) [From Stephen Crowley (crow(AT)crowlogic.net), Jun 28 2009]
G.f.:-x^2*(4*x^2+7*x+1)/(x-1)^5 [From Maksym Voznyy (voznyy(AT)mail.ru), Aug 11 2009]
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MAPLE
| f := n->n*(n-1)^3/2;
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MATHEMATICA
| f[n_]:=n*(n-1)^3/2; Table[f[n], {n, 0, 4!}] [From Vladimir Orlovsky (4vladimir(AT)gmail.com), Apr 08 2010]
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PROG
| (MAGMA) [n*(n-1)^3/2: n in [0..60]]; // Vincenzo Librandi, Apr 26 2011
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CROSSREFS
| Cf. A000217, A000290.
A row or column of A132191.
Sequence in context: A060785 A059986 A088941 * A025204 A005549 A124858
Adjacent sequences: A019579 A019580 A019581 * A019583 A019584 A019585
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KEYWORD
| nonn
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AUTHOR
| N. J. A. Sloane (njas(AT)research.att.com).
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EXTENSIONS
| hypergeometric zeta formula [From Stephen Crowley (crow(AT)crowlogic.net), Jun 28 2009]
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