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

Offset

0,5

Comments

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

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).

Example

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

Prog

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

Crossrefs

Cf. A007318.

Sequence in context: A133824 A154228 A141697 * A177823 A142462 A203397

Adjacent sequences: A202747 A202748 A202749 * A202751 A202752 A202753

Keyword

nonn,easy,tabl

Author

Charles R Greathouse IV, Dec 23 2011

Status

approved