A202750 - OEIS

%I #15 Mar 30 2012 17:28:27

%S 1,1,1,1,16,1,1,81,81,1,1,256,1296,256,1,1,625,10000,10000,625,1,1,

%T 1296,50625,160000,50625,1296,1,1,2401,194481,1500625,1500625,194481,

%U 2401,1,1,4096,614656,9834496,24010000,9834496,614656,4096,1,1,6561,1679616

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

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

%H Vincenzo Librandi, <a href="/A202750/b202750.txt">Rows n = 1..21, flattened</a>

%H Zhi-Wei Sun, <a href="http://arxiv.org/abs/1103.4325">Conjectures and results on x^2 mod p^2 with 4p=x^2+dy^2</a> (2011).

%e Interpreted as polynomials:

%e 1

%e x + 1

%e x^2 + 16*x + 1

%e x^3 + 81*x^2 + 81*x + 1

%e x^4 + 256*x^3 + 1296*x^2 + 256*x + 1

%e x^5 + 625*x^4 + 10000*x^3 + 10000*x^2 + 625*x + 1

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

%Y Cf. A007318.

%K nonn,easy,tabl

%O 0,5

%A _Charles R Greathouse IV_, Dec 23 2011