A355267 Triangle read by rows, T(n, k) = n! * [y^k] [x^n] exp(1/(1 - x)^(1 + y) - 1), for 0 <= k <= n.

1, 1, 1, 3, 5, 2, 13, 29, 21, 5, 73, 200, 202, 90, 15, 501, 1609, 2045, 1295, 410, 52, 4051, 14809, 22418, 18085, 8220, 1998, 203, 37633, 153453, 267400, 259175, 151165, 53095, 10402, 877, 394353, 1767240, 3463612, 3889620, 2740885, 1241632, 353178, 57676, 4140

Offset: 0

Author

Peter Luschny, Jul 05 2022

Keywords

• nonn
• tabl

Examples

			Triangle T(n, k) begins:
[0]      1;
[1]      1,      1;
[2]      3,      5,      2;
[3]     13,     29,     21,      5;
[4]     73,    200,    202,     90,     15;
[5]    501,   1609,   2045,   1295,    410,    52;
[6]   4051,  14809,  22418,  18085,   8220,  1998,   203;
[7]  37633, 153453, 267400, 259175, 151165, 53095, 10402, 877;
		

Crossrefs

Cf. A136658 (row sums), A000007 (alternating row sums), A000262 (column 0), A216313 (column 1), A000110 (main diagonal).

Cf. A355260.

Programs

Maple

egf := exp(1/(1 - x)^(1 + y) - 1):
ser := series(egf, x, 12): cfx := n -> coeff(ser, x, n):
seq(print(seq(n!*(coeff(cfx(n), y, k)), k = 0..n)), n = 0..8);