A187017 Array where the n-th row is the expansion of (1+2*x+...+n*x^(n-1)) * (n+(n-1)*x+...+x^(n-1)).

1, 2, 5, 2, 3, 8, 14, 8, 3, 4, 11, 20, 30, 20, 11, 4, 5, 14, 26, 40, 55, 40, 26, 14, 5, 6, 17, 32, 50, 70, 91, 70, 50, 32, 17, 6, 7, 20, 38, 60, 85, 112, 140, 112, 85, 60, 38, 20, 7, 8, 23, 44, 70, 100, 133, 168, 204, 168, 133, 100, 70, 44, 23, 8, 9, 26, 50, 80, 115, 154, 196, 240, 285, 240, 196, 154, 115, 80, 50, 26, 9

Offset: 1

Author

Franklin T. Adams-Watters, Mar 02 2011

Keywords

• nonn
• tabf
• easy

Examples

			The table starts:
1
2 5 2
3 8 14 8 3
4 11 20 30 20 11 4
		

Crossrefs

Cf. A005408(row lengths), A000537(row sums), A115262(a rearrangement), A000330(central diagonal).

Programs

PARI

al(n)=Vec(sum(k=1,n,k*x^(k-1))*sum(k=1,n,k*x^(n-k)))