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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!. 1
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified May 8 09:21 EDT 2021. Contains 343666 sequences. (Running on oeis4.)