0,2

Row sums form A099606, where A099606(n) = Pell(n+1)*2^[(n+1)/2]. Central coefficients of even-indexed rows form A026000, where A026000(n) = T(2n,n), where T = Delannoy triangle (A008288). Antidiagonal sums form A099607.

G.f.: (1+2*(y+1)*x-(y+1)*x^2)/(1-(2*y+1)*(2*y+2)*x^2+(y+1)^2*x^4). T(n, n) = 2^n.

Rows begin:

[1],

[2,2],

[1,5,4],

[4,16,20,8],

[1,14,41,44,16],

[6,50,146,198,128,32],

[1,27,155,377,456,272,64],

[8,112,560,1408,1992,1616,704,128],

[1,44,406,1652,3649,4712,3568,1472,256],

[10,210,1572,6084,14002,20330,18880,10912,3584,512],

[1,65,870,5202,17469,36365,48940,42800,23552,7424,1024],...

The binomial transform of row 2 equals column 2 of A034870:

BINOMIAL[1,5,4] = [1,6,15,28,45,66,91,120,153,...].

The binomial transform of row 3 equals column 3 of A034870:

BINOMIAL[4,16,20,8] = [4,20,56,120,220,364,560,...].

The binomial transform of row 4 equals column 4 of A034870:

BINOMIAL[1,14,41,44,16] = [1,15,70,210,495,1001,...].

(PARI) {T(n, k)=polcoeff(polcoeff((1+2*(y+1)*x-(y+1)*x^2)/(1-(2*y+1)*(2*y+2)*x^2+(y+1)^2*x^4)+x*O(x^n), n, x)+y*O(y^k), k, y)}

Cf. A099602, A099605, A034870, A000129.

Sequence in context: A125178 A101975 A136388 this_sequence A079218 A079220 A123971

Adjacent sequences: A099602 A099603 A099604 this_sequence A099606 A099607 A099608

nonn,tabl

Paul D. Hanna (pauldhanna(AT)juno.com), Oct 25 2004