A131820 - OEIS

A131820

Row sums of triangle A131819.

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

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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

LINKS

Table of n, a(n) for n=1..42.

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.