A220267 Main diagonal of triangle A220265.

1, 9, 177, 9800, 1131750, 225598527, 69153712446, 30211650109440, 17832410391617082, 13670065258130703125, 13203133188522251881137, 15685246720965582029887488, 22477297594725738707224270105, 38231902029181930196176183861755, 76144787589417130318451646093750000

Offset: 1

Author

Paul D. Hanna, Dec 09 2012

Keywords

• nonn

Comments

G.f. of row n of triangle A220265 equals: Sum_{k=0..n^2-n+1} A220265(n,k)*y^k = (2*(1+y)^n - 1)*((1+y)^n - 1)^(n-1)/y^(n-1) for n>=1.

Examples

			 Irregular triangle A220265 begins:
1, 2;
2, 9, 8, 2;
9, 72, 177, 222, 163, 72, 18, 2;
64, 800, 3696, 9800, 17408, 22284, 21340, 15554, 8652, 3633, 1120, 240, 32, 2;
625, 11250, 82500, 365000, 1131750, 2654250, 4922750, 7425000, 9274150, 9704600, 8566200, 6398000, 4042345, 2152890, 959690, 354020, 106251, 25300, 4600, 600, 50, 2; ...
		

Crossrefs

Cf. A220265, A220266.

Programs

PARI

{a(n)=polcoeff((2*(1+x)^n-1)*((1+x)^n-1)^(n-1)/x^(n-1), n-1)}
for(n=1, 20, print1(a(n), ", "))

Formula

a(n) = A220265(n,n-1) for n>=1.