A084602 Triangle, read by rows, where the n-th row lists the (2n+1) coefficients of (1 + x + 3x^2)^n.

1, 1, 1, 3, 1, 2, 7, 6, 9, 1, 3, 12, 19, 36, 27, 27, 1, 4, 18, 40, 91, 120, 162, 108, 81, 1, 5, 25, 70, 185, 331, 555, 630, 675, 405, 243, 1, 6, 33, 110, 330, 726, 1441, 2178, 2970, 2970, 2673, 1458, 729, 1, 7, 42, 161, 539, 1386, 3157, 5797, 9471, 12474, 14553

Offset: 0

Author

Paul D. Hanna, Jun 01 2003

Keywords

• nonn
• tabf

Examples

			Rows:
{1},
{1,1, 3},
{1,2, 7,  6,  9},
{1,3,12, 19, 36, 27,  27},
{1,4,18, 40, 91,120, 162, 108,  81},
{1,5,25, 70,185,331, 555, 630, 675, 405, 243},
{1,6,33,110,330,726,1441,2178,2970,2970,2673,1458,729},
		

Links

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

Crossrefs

Cf. A002426, A084600-A084601, A084603-A084615.

Programs

Mathematica

With[{eq = (1 + x + 3*x^2)}, Flatten[Table[CoefficientList[Expand[eq^n], x], {n, 0, 10}]]] (* G. C. Greubel, Mar 02 2017 *)

PARI

for(n=0,15, for(k=0,2*n,t=polcoeff((1+x+3*x^2)^n,k,x); print1(t",")); print(" "))