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Search: id:A019582
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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; listen)
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OFFSET
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0,4
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COMMENT
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a(n)=n(n-1)^3/2 is half the number of colorings of 4 points on a line with n colors. - Ron Hardin (rhh(AT)cadence.com), 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
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FORMULA
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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
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MAPLE
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f := n->n*(n-1)^3/2;
seq (n^2*(stirling2(n+1, n)), n=-1..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Jan 20 2007
a:=n->sum(n^2*j, j=0..n): seq(a(n), n=-1..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
a:=n->sum(sum(n^2/2, j=1..n), k=0..n): seq(a(n), n=-1..29); - Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), May 09 2007
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CROSSREFS
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Cf. A000217, A000290.
A row or column of A132191.
Sequence in context: A060785 A059986 A088941 this_sequence A025204 A005549 A124858
Adjacent sequences: A019579 A019580 A019581 this_sequence A019583 A019584 A019585
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KEYWORD
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nonn
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AUTHOR
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njas
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