A084604 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1 + x + 4x^2)^n.

1, 1, 1, 4, 1, 2, 9, 8, 16, 1, 3, 15, 25, 60, 48, 64, 1, 4, 22, 52, 145, 208, 352, 256, 256, 1, 5, 30, 90, 285, 561, 1140, 1440, 1920, 1280, 1024, 1, 6, 39, 140, 495, 1206, 2841, 4824, 7920, 8960, 9984, 6144, 4096, 1, 7, 49, 203, 791, 2261, 6027, 12489, 24108, 36176

Offset: 0

Author

Paul D. Hanna, Jun 01 2003

Keywords

• nonn
• tabf

Examples

			Rows:
{1},
{1,1, 4},
{1,2, 9,  8, 16},
{1,3,15, 25, 60,  48,  64},
{1,4,22, 52,145, 208, 352, 256, 256},
{1,5,30, 90,285, 561,1140,1440,1920,1280,1024},
{1,6,39,140,495,1206,2841,4824,7920,8960,9984,6144,4096},
		

Links

• G. C. Greubel, Table of n, a(n) for the first 50 rows, flattened

Crossrefs

Cf. A002426, A084600-A084603, A084605-A084615.

Programs

Mathematica

With[{eq=(1+x+4x^2)},Flatten[Table[CoefficientList[Expand[eq^n],x],{n,0,10}]]] (* Harvey P. Dale, May 19 2011 *)

PARI

for(n=0,10, for(k=0,2*n,t=polcoeff((1+x+4*x^2)^n,k,x); print1(t",")); print(" "))