A099904 Numerator of sum of all matrix elements of N X N matrix M(i,j) = i^3+j^3, (i,j = 1..n) divided by n!.

2, 18, 36, 100, 75, 147, 98, 18, 45, 605, 121, 169, 1183, 7, 1, 289, 289, 361, 361, 1, 11, 5819, 529, 1, 13, 13, 1, 841, 841, 961, 961, 1, 17, 17, 1, 1369, 26011, 19, 1, 1681, 1681, 1849, 1849, 1, 23, 50807, 2209, 1, 1, 1, 1, 2809, 2809, 1, 1, 1, 29, 100949, 3481, 3721

Offset: 1

Author

Alexander Adamchuk, Oct 29 2004

Keywords

• nonn

Comments

Sum M(i,j) (i,j = 1..n) is A099903(n). a(n) is an irregular sequence with highest champions belonging to Pentagonal pyramidal numbers n^2*(n+1)/2 (A002411) and n/2*(n+1)^2 (A006002).

Examples

			A099903(n)/n! begins 2, 18, 36, 100/3, 75/4, 147/20, 98/45, 18/35, 45/448, ... So a(6) = 147.
		

Crossrefs

Cf. A099903, A019584, A098077, A002411, A006002.

Programs

Mathematica

Table[ Numerator[ Sum[(i^3 + j^3), {i, n}, {j, n}]/n! ], {n, 60}]

Formula

a(n) = Numerator[1/n!*Sum[Sum[(i^3+j^3), {i, 1, n}], {j, 1, n}]] a(n) = Numerator[1/2 * (n^3)*(n+1)^2 /n! ].