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

1,1

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).

Links

Table of n, a(n) for n=1..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! ].

Example

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

Mathematica

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

Crossrefs

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

Sequence in context: A073213 A086490 A085876 * A137308 A050594 A098857

Adjacent sequences: A099901 A099902 A099903 * A099905 A099906 A099907

Keyword

nonn

Author

Alexander Adamchuk, Oct 29 2004

Status

approved