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

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.

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

Cf. A131819, A000330, A081489, A005563.

Sequence in context: A118014 A361230 A236773 * A266677 A083053 A083046

Adjacent sequences: A131817 A131818 A131819 * A131821 A131822 A131823

Keyword

nonn

Author

Gary W. Adamson, Jul 18 2007

Extensions

More terms from Alois P. Heinz, May 04 2009

Status

approved