A154226 List of pairs: {(n*(n+1)/2)^2, (n!)^3}.

0, 1, 1, 1, 9, 8, 36, 216, 100, 13824, 225, 1728000, 441, 373248000, 784, 128024064000, 1296, 65548320768000, 2025, 47784725839872000, 3025, 47784725839872000000, 4356, 63601470092869632000000, 6084

Offset: 0

Author

Roger L. Bagula, Jan 05 2009

Keywords

• nonn
• easy
• less

Links

• G. C. Greubel, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000442, A000537.

Programs

Magma

&cat[[(n*(n+1)/2)^2, Factorial(n)^3]: n in [0..15]]; // Vincenzo Librandi, Sep 07 2016

Mathematica

a[0] = 0; a[n_] := a[n] = n^3 + a[n - 1];
b[0] = 1; b[n_] := b[n] = n^3*b[n - 1];
Flatten[Table[{a[n], b[n]}, {n, 0, 15}]]

Formula

a(2n+1) = A000442(n) = (n!)^3.

a(2n) = A000537(n) = (n*(n+1)/2)^2.