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

0,3

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)

Links

Table of n, a(n) for n=0..18.

Formula

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

Mathematica

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

Crossrefs

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

Sequence in context: A238844 A073852 A139033 * A001044 A306736 A307845

Adjacent sequences: A370750 A370751 A370752 * A370754 A370755 A370756

Keyword

nonn

Author

Stefano Spezia, Jun 22 2024

Status

approved