A154226 - OEIS

%I #21 Sep 08 2022 08:45:40

%S 0,1,1,1,9,8,36,216,100,13824,225,1728000,441,373248000,784,

%T 128024064000,1296,65548320768000,2025,47784725839872000,3025,

%U 47784725839872000000,4356,63601470092869632000000,6084

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

%H G. C. Greubel, <a href="/A154226/b154226.txt">Table of n, a(n) for n = 0..500</a>

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

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

%t a[0] = 0; a[n_] := a[n] = n^3 + a[n - 1];

%t b[0] = 1; b[n_] := b[n] = n^3*b[n - 1];

%t Flatten[Table[{a[n], b[n]}, {n, 0, 15}]]

%o (Magma) &cat[[(n*(n+1)/2)^2, Factorial(n)^3]: n in [0..15]]; // _Vincenzo Librandi_, Sep 07 2016

%Y Cf. A000442, A000537.

%K nonn,easy,less

%O 0,5

%A _Roger L. Bagula_, Jan 05 2009