A350594 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where T(n,k) is Sum_{j=0..2*n} (-1)^(n+j) * binomial(2*n,j)^k.

1, 1, -1, 1, 0, 1, 1, 2, 0, -1, 1, 6, 6, 0, 1, 1, 14, 90, 20, 0, -1, 1, 30, 786, 1680, 70, 0, 1, 1, 62, 5730, 61340, 34650, 252, 0, -1, 1, 126, 38466, 1696800, 5562130, 756756, 924, 0, 1, 1, 254, 247170, 41312060, 613591650, 549676764, 17153136, 3432, 0, -1

Offset: 0

Author

Seiichi Manyama, Jan 08 2022

Keywords

• sign
• tabl

Examples

			Square array begins:
   1, 1,   1,      1,         1,            1, ...
  -1, 0,   2,      6,        14,           30, ...
   1, 0,   6,     90,       786,         5730, ...
  -1, 0,  20,   1680,     61340,      1696800, ...
   1, 0,  70,  34650,   5562130,    613591650, ...
  -1, 0, 252, 756756, 549676764, 248832363780, ...
		

Links

• Seiichi Manyama, Antidiagonals n = 0..50, flattened

Crossrefs

Columns k=0..6 give A033999, A000007, A000984, A006480, A050983, A050984, A227357.

Rows n=0..1 give A000012, A000918.

Main diagonal gives A350595.

Cf. A257050, A309010.

Programs

PARI

T(n, k) = sum(j=0, 2*n, (-1)^(n+j)*binomial(2*n, j)^k);