A370753 Antidiagonal products of A319840.

1, 1, 4, 36, 576, 12800, 360000, 12192768, 481890304, 21743271936, 1101996057600, 61952000000000, 3824628881965056, 257164113195565056, 18704075505689706496, 1462975070062038220800, 122444006400000000000000, 10918111308394619734065152, 1033255398127440061257744384

Offset: 0

Author

Stefano Spezia, Jun 22 2024

Keywords

• nonn

Comments

a(n) has trailing zeros iff n is congruent to 0 or 1 mod 5. Cf. A008851.

a(n) is a square iff n = 1 or congruent to {1, 3, 4} mod 5. Cf. A047206.

It appears that: (Start)

a(n) is a cube iff n = 0, 1, or is of the form (3*m - 4)^3 with m > 1 (A016791);

the only fourth powers in the sequence are 1 and a(9) = 21743271936 = 384^4;

the only fifth powers in the sequence are 1 and a(32) = 227200942336^5;

a(n) is a sixth power iff n = 0, 1, or is of the form (6*m - 10)^3 with m > 1;

the only seventh powers in the sequence are 1 and a(128) = 77458109039896212820250015287665035595218944^7. (End)

Crossrefs

Cf. A000079, A000169, A000290, A008851, A016791, A047206, A319840.

Programs

Mathematica

a[0]=a[1]=1; a[n_]:=n^2*2^(n-2)*(n-1)^(n-2); Array[a,19,0]

Formula

a(0) = a(1) = 1, and a(n) = n^2*2^(n-2)*(n - 1)^(n-2) for n > 1.