A355267 - OEIS

%I #7 Jul 06 2022 11:10:37

%S 1,1,1,3,5,2,13,29,21,5,73,200,202,90,15,501,1609,2045,1295,410,52,

%T 4051,14809,22418,18085,8220,1998,203,37633,153453,267400,259175,

%U 151165,53095,10402,877,394353,1767240,3463612,3889620,2740885,1241632,353178,57676,4140

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

%e Triangle T(n, k) begins:

%e [0]      1;

%e [1]      1,      1;

%e [2]      3,      5,      2;

%e [3]     13,     29,     21,      5;

%e [4]     73,    200,    202,     90,     15;

%e [5]    501,   1609,   2045,   1295,    410,    52;

%e [6]   4051,  14809,  22418,  18085,   8220,  1998,   203;

%e [7]  37633, 153453, 267400, 259175, 151165, 53095, 10402, 877;

%p egf := exp(1/(1 - x)^(1 + y) - 1):

%p ser := series(egf, x, 12): cfx := n -> coeff(ser, x, n):

%p seq(print(seq(n!*(coeff(cfx(n), y, k)), k = 0..n)), n = 0..8);

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

%Y Cf. A355260.

%K nonn,tabl

%O 0,4

%A _Peter Luschny_, Jul 05 2022