A099095 - OEIS

%I #6 Jul 07 2012 13:03:20

%S 1,0,3,0,2,9,0,0,12,27,0,0,4,54,81,0,0,0,36,216,243,0,0,0,8,216,810,

%T 729,0,0,0,0,96,1080,2916,2187,0,0,0,0,16,720,4860,10206,6561,0,0,0,0,

%U 0,240,4320,20412,34992,19683,0,0,0,0,0,32,2160,22680,81648,118098,59049,0,0

%N Riordan array (1,3+2x).

%C Row sums are A007482. Diagonal sums are A053088. The Riordan array (1,s+tx) defines T(n,k)=binomial(k,n-k)s^k(t/s)^(n-k). The row sums satisfy a(n)=s*a(n-1)+t*a(n-2) and the diagonal sums satisfy a(n)=s*a(n-2)+t*a(n-3).

%H Eric W. Weisstein, <a href="http://mathworld.wolfram.com/FermatPolynomial.html">Fermat Polynomial</a>

%F Number triangle T(n, k)=binomial(k, n-k)3^k*(2/3)^(n-k); Columns have g.f. (3x+2x^2)^k.

%e Rows begin {1}, {0,3}, {0,2,9}, {0,0,12,27}, {0,0,4,54,81},...

%Y Cf. A038220.

%K easy,nonn,tabl

%O 0,3

%A _Paul Barry_, Sep 25 2004