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A131820
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Row sums of triangle A131819.
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2
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1, 6, 16, 33, 59, 96, 146, 211, 293, 394, 516, 661, 831, 1028, 1254, 1511, 1801, 2126, 2488, 2889, 3331, 3816, 4346, 4923, 5549, 6226, 6956, 7741, 8583, 9484, 10446, 11471, 12561, 13718, 14944, 16241, 17611, 19056, 20578, 22179, 23861, 25626
(list; graph; refs; listen; history; internal format)
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OFFSET
| 1,2
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COMMENTS
| a(n) = a(n-1) + n^2 + 1, n> 1 [From Gary Detlefs, Jun 30 2010]
Let M(n) be the nth square matrix whose (i,j)-entry equals i^2/(i^2+1) if i=j and equals 1 otherwise. Then a(n)=(-1)^(n+1) * gamma(1-i+n) * gamma(1+i+n) * sinh(pi)/pi times the determinant of M(n). [From John M. Campbell, Sep 07 2011]
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FORMULA
| Binomial transform of (1, 5, 5, 2, 0, 0, 0,...).
Contribution from Alois P. Heinz, May 04 2009: (Start)
a(n) = n^3/3 + n^2/2 + 7/6*n - 1.
a(n) = -1 + Sum_{k=1..n} (k^2+1).
a(n) = A000330(n) + A000027(n) - A000012(n).
G.f.: (2*x^3-4*x^2+5*x-1) / (x-1)^4. (End)
a(n) = (2n^3 + 3n^2 + 7n - 6)/6, n>0. [From Gary Detlefs, Jun 30 2010]
a(n) = n^2+a(n-1)+1, n>1. [From Gary Detlefs, Jun 29 2010]
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EXAMPLE
| a(4) = 33 = (1, 3, 3, 1) dot (1, 5, 5, 2) = (1 + 15 + 15 + 2).
a(4) = 33 = sum of row 4 terms of triangle A131819: (13 + 9 + 7 + 4).
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MAPLE
| a:= n-> (7+(3+2*n)*n)*n/6-1: seq (a(n), n=1..40); # Alois P. Heinz, May 04 2009
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MATHEMATICA
| Table[n^3/3 + n^2/2 + 7*n/6 - 1, {n, 100}]
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CROSSREFS
| Cf. A131819.
A131820(n) = A081489(n) + A005563(n-1), n>0. - Gary Detlefs, Jun 30 2010
Sequence in context: A071857 A099399 A118014 * A083053 A083046 A192749
Adjacent sequences: A131817 A131818 A131819 * A131821 A131822 A131823
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KEYWORD
| nonn
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AUTHOR
| Gary W. Adamson (qntmpkt(AT)yahoo.com), Jul 18 2007
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EXTENSIONS
| More terms from Alois P. Heinz (heinz(AT)hs-heilbronn.de), May 04 2009
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