A202750 Triangle T(n,k) = binomial(n,k)^4 read by rows, 0<=k<=n.

1, 1, 1, 1, 16, 1, 1, 81, 81, 1, 1, 256, 1296, 256, 1, 1, 625, 10000, 10000, 625, 1, 1, 1296, 50625, 160000, 50625, 1296, 1, 1, 2401, 194481, 1500625, 1500625, 194481, 2401, 1, 1, 4096, 614656, 9834496, 24010000, 9834496, 614656, 4096, 1, 1, 6561, 1679616, 49787136, 252047376, 252047376, 49787136, 1679616, 6561, 1

Offset: 0

Author

Charles R Greathouse IV, Dec 23 2011

Keywords

• nonn
• easy
• tabl

Comments

Zhi-Wei Sun has conjectures related to the arithmetic mean of the polynomials formed from the rows of this sequence.

Examples

			Interpreted as polynomials:
1
x + 1
x^2 + 16*x + 1
x^3 + 81*x^2 + 81*x + 1
x^4 + 256*x^3 + 1296*x^2 + 256*x + 1
x^5 + 625*x^4 + 10000*x^3 + 10000*x^2 + 625*x + 1
		

Links

• Vincenzo Librandi, Rows n = 1..21, flattened
• Zhi-Wei Sun, Conjectures and results on x^2 mod p^2 with 4p=x^2+dy^2 (2011).

Crossrefs

Cf. A007318.

Row sums give A005260.

Programs

PARI

for(n=0,9,for(k=0,n,print1(binomial(n,k)^4", ")))