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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.

%I A355267 #7 Jul 06 2022 11:10:37
%S A355267 1,1,1,3,5,2,13,29,21,5,73,200,202,90,15,501,1609,2045,1295,410,52,
%T A355267 4051,14809,22418,18085,8220,1998,203,37633,153453,267400,259175,
%U A355267 151165,53095,10402,877,394353,1767240,3463612,3889620,2740885,1241632,353178,57676,4140
%N A355267 Triangle read by rows, T(n, k) = n! * [y^k] [x^n] exp(1/(1 - x)^(1 + y) - 1), for 0 <= k <= n.
%e A355267 Triangle T(n, k) begins:
%e A355267 [0]      1;
%e A355267 [1]      1,      1;
%e A355267 [2]      3,      5,      2;
%e A355267 [3]     13,     29,     21,      5;
%e A355267 [4]     73,    200,    202,     90,     15;
%e A355267 [5]    501,   1609,   2045,   1295,    410,    52;
%e A355267 [6]   4051,  14809,  22418,  18085,   8220,  1998,   203;
%e A355267 [7]  37633, 153453, 267400, 259175, 151165, 53095, 10402, 877;
%p A355267 egf := exp(1/(1 - x)^(1 + y) - 1):
%p A355267 ser := series(egf, x, 12): cfx := n -> coeff(ser, x, n):
%p A355267 seq(print(seq(n!*(coeff(cfx(n), y, k)), k = 0..n)), n = 0..8);
%Y A355267 Cf. A136658 (row sums), A000007 (alternating row sums), A000262 (column 0), A216313 (column 1), A000110 (main diagonal).
%Y A355267 Cf. A355260.
%K A355267 nonn,tabl
%O A355267 0,4
%A A355267 _Peter Luschny_, Jul 05 2022