cp's OEIS Frontend

A355427 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - Sum_{j=1..k} (exp(j*x) - 1)/j).

%I A355427 #14 Jul 02 2022 09:06:33
%S A355427 1,1,0,1,1,0,1,2,3,0,1,3,11,13,0,1,4,24,89,75,0,1,5,42,284,959,541,0,
%T A355427 1,6,65,654,4476,12917,4683,0,1,7,93,1255,13564,88178,208781,47293,0,
%U A355427 1,8,126,2143,32275,351634,2084564,3937019,545835,0
%N A355427 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals, where column k is the expansion of e.g.f. 1/(1 - Sum_{j=1..k} (exp(j*x) - 1)/j).
%F A355427 T(0,k) = 1 and T(n,k) = Sum_{i=1..n} (Sum_{j=1..k} j^(i-1)) * binomial(n,i) * T(n-i,k) for n > 0.
%e A355427 Square array begins:
%e A355427   1,   1,     1,     1,      1,       1, ...
%e A355427   0,   1,     2,     3,      4,       5, ...
%e A355427   0,   3,    11,    24,     42,      65, ...
%e A355427   0,  13,    89,   284,    654,    1255, ...
%e A355427   0,  75,   959,  4476,  13564,   32275, ...
%e A355427   0, 541, 12917, 88178, 351634, 1037479, ...
%Y A355427 Columns k=0..3 give A000007, A000670, A355425, A355426.
%Y A355427 Main diagonal gives A355428.
%Y A355427 Cf. A306024, A320253.
%K A355427 nonn,tabl
%O A355427 0,8
%A A355427 _Seiichi Manyama_, Jul 01 2022