cp's OEIS Frontend

A383064 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of e.g.f. Sum_{j>=0} (j+1)^k * (-log(1-x))^j / j!.

%I A383064 #12 Apr 15 2025 08:26:29
%S A383064 1,1,1,1,2,2,1,4,5,6,1,8,13,17,24,1,16,35,51,74,120,1,32,97,161,244,
%T A383064 394,720,1,64,275,531,854,1392,2484,5040,1,128,793,1817,3148,5248,
%U A383064 9260,18108,40320,1,256,2315,6411,12134,20940,36966,70508,149904,362880
%N A383064 Square array A(n,k), n>=0, k>=0, read by antidiagonals downwards, where column k is the expansion of e.g.f. Sum_{j>=0} (j+1)^k * (-log(1-x))^j / j!.
%F A383064 See A344639.
%e A383064 Square array begins:
%e A383064     1,    1,    1,     1,      1,      1,       1, ...
%e A383064     1,    2,    4,     8,     16,     32,      64, ...
%e A383064     2,    5,   13,    35,     97,    275,     793, ...
%e A383064     6,   17,   51,   161,    531,   1817,    6411, ...
%e A383064    24,   74,  244,   854,   3148,  12134,   48604, ...
%e A383064   120,  394, 1392,  5248,  20940,  87784,  384252, ...
%e A383064   720, 2484, 9260, 36966, 156680, 699894, 3274640, ...
%o A383064 (PARI) a(n, k) = sum(j=0, n, j!*abs(stirling(n+1, j+1, 1))*stirling(k+1, j+1, 2));
%Y A383064 Mirror of A344639.
%Y A383064 Main diagonal gives A192563.
%K A383064 nonn,tabl
%O A383064 0,5
%A A383064 _Seiichi Manyama_, Apr 15 2025