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A368506
Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) = Sum_{j=0..n} k^(n-j) * binomial(j+k-1,j).
0
1, 1, 0, 1, 2, 0, 1, 4, 3, 0, 1, 6, 11, 4, 0, 1, 8, 24, 26, 5, 0, 1, 10, 42, 82, 57, 6, 0, 1, 12, 65, 188, 261, 120, 7, 0, 1, 14, 93, 360, 787, 804, 247, 8, 0, 1, 16, 126, 614, 1870, 3204, 2440, 502, 9, 0, 1, 18, 164, 966, 3810, 9476, 12900, 7356, 1013, 10, 0
OFFSET
0,5
FORMULA
G.f. of column k: 1/((1-k*x) * (1-x)^k).
EXAMPLE
Square array begins:
1, 1, 1, 1, 1, 1, 1, ...
0, 2, 4, 6, 8, 10, 12, ...
0, 3, 11, 24, 42, 65, 93, ...
0, 4, 26, 82, 188, 360, 614, ...
0, 5, 57, 261, 787, 1870, 3810, ...
0, 6, 120, 804, 3204, 9476, 23112, ...
0, 7, 247, 2440, 12900, 47590, 139134, ...
PROG
(PARI) T(n, k) = sum(j=0, n, k^(n-j)*binomial(j+k-1, j));
CROSSREFS
Columns k=0..3 give A000007, A000027(n+1), A125128(n+1), A052150.
Main diagonal gives A293574.
Sequence in context: A124912 A138752 A357499 * A342133 A358050 A334781
KEYWORD
nonn,tabl
AUTHOR
Seiichi Manyama, Dec 27 2023
STATUS
approved