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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.
2
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
0,8
LINKS
EXAMPLE
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, ...
PROG
(PARI) T(n, k) = sum(j=0, 2*n, (-1)^(n+j)*binomial(2*n, j)^k);
CROSSREFS
Columns k=0..6 give A033999, A000007, A000984, A006480, A050983, A050984, A227357.
Rows n=0..1 give A000012, A000918.
Main diagonal gives A350595.
Sequence in context: A228748 A343464 A225094 * A295859 A180160 A101661
KEYWORD
sign,tabl
AUTHOR
Seiichi Manyama, Jan 08 2022
STATUS
approved