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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, 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
0,4
EXAMPLE
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;
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);
CROSSREFS
Cf. A136658 (row sums), A000007 (alternating row sums), A000262 (column 0), A216313 (column 1), A000110 (main diagonal).
Cf. A355260.
Sequence in context: A325891 A217859 A108426 * A301305 A163237 A053979
KEYWORD
nonn,tabl
AUTHOR
Peter Luschny, Jul 05 2022
STATUS
approved