A261642 Triangle, read by rows, where T(n,k) = (k^2 + k)^(n-k) for k=1..n and n>=1.

1, 2, 1, 4, 6, 1, 8, 36, 12, 1, 16, 216, 144, 20, 1, 32, 1296, 1728, 400, 30, 1, 64, 7776, 20736, 8000, 900, 42, 1, 128, 46656, 248832, 160000, 27000, 1764, 56, 1, 256, 279936, 2985984, 3200000, 810000, 74088, 3136, 72, 1, 512, 1679616, 35831808, 64000000, 24300000, 3111696, 175616, 5184, 90, 1

Offset: 1

Author

Paul D. Hanna, Aug 27 2015

Keywords

• nonn
• tabl

Comments

Matrix inverse of triangle P with element P(n,k) = (-1)^(n-k) * (k^2 + k)^(n-k) / (n-k)! forms triangle A103244.

Examples

			This triangle begins:
1;
2, 1;
4, 6, 1;
8, 36, 12, 1;
16, 216, 144, 20, 1;
32, 1296, 1728, 400, 30, 1;
64, 7776, 20736, 8000, 900, 42, 1;
128, 46656, 248832, 160000, 27000, 1764, 56, 1;
256, 279936, 2985984, 3200000, 810000, 74088, 3136, 72, 1;
512, 1679616, 35831808, 64000000, 24300000, 3111696, 175616, 5184, 90, 1;
1024, 10077696, 429981696, 1280000000, 729000000, 130691232, 9834496, 373248, 8100, 110, 1; ...
		

Crossrefs

Cf. A103244, A261643 (row sums).

Programs

PARI

{T(n, k) = (k^2 + k)^(n-k)}
for(n=1, 10, for(k=1, n, print1(T(n, k), ", ")); print(""))