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A131820
Row sums of triangle A131819.
1
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
OFFSET
1,2
COMMENTS
Let M(n) be the n-th 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). - John M. Campbell, Sep 07 2011
FORMULA
Binomial transform of (1, 5, 5, 2, 0, 0, 0, ...).
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) = n^2 + a(n-1) + 1, n > 1. - Gary Detlefs, Jun 29 2010
From Gary Detlefs, Jun 30 2010: (Start)
a(n) = (2n^3 + 3n^2 + 7n - 6)/6, n > 0.
a(n) = A081489(n) + A005563(n-1), n > 0. (End)
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).
MAPLE
a:= n-> (7+(3+2*n)*n)*n/6-1:
seq(a(n), n=1..40); # Alois P. Heinz, May 04 2009
MATHEMATICA
Table[n^3/3 + n^2/2 + 7*n/6 - 1, {n, 100}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Gary W. Adamson, Jul 18 2007
EXTENSIONS
More terms from Alois P. Heinz, May 04 2009
STATUS
approved