cp's OEIS Frontend

A360753 Matrix inverse of A360657.

%I A360753 #23 Feb 24 2023 01:56:42
%S A360753 1,0,1,0,-2,1,0,1,-5,1,0,1,8,-9,1,0,2,4,29,-14,1,0,6,4,-10,75,-20,1,0,
%T A360753 24,4,-41,-115,160,-27,1,0,120,-8,-147,-196,-490,301,-35,1,0,720,-136,
%U A360753 -624,-392,-231,-1484,518,-44,1
%N A360753 Matrix inverse of A360657.
%F A360753 Conjectured formulas:
%F A360753 1. Matrix product of A354794 and T without column 0 equals A215534.
%F A360753 2. Matrix product of T and A354794 without column 0 equals A132013.
%F A360753 3. E.g.f. of column k > 0: Sum_{n >= k} T(n, k) * t^(n-1) / (n-1)! = (1 - t) * (Sum_{n >= k} A354795(n, k) * t^(n-1) / (n-1)!).
%e A360753 Triangle T(n, k) for 0 <= k <= n starts:
%e A360753 n\k :  0    1     2     3     4     5      6    7    8  9
%e A360753 =========================================================
%e A360753   0 :  1
%e A360753   1 :  0    1
%e A360753   2 :  0   -2     1
%e A360753   3 :  0    1    -5     1
%e A360753   4 :  0    1     8    -9     1
%e A360753   5 :  0    2     4    29   -14     1
%e A360753   6 :  0    6     4   -10    75   -20      1
%e A360753   7 :  0   24     4   -41  -115   160    -27    1
%e A360753   8 :  0  120    -8  -147  -196  -490    301  -35    1
%e A360753   9 :  0  720  -136  -624  -392  -231  -1484  518  -44  1
%e A360753   etc.
%o A360753 (PARI) tabl(m) = {my(n=2*m, A = matid(n), B, C, T); for( i = 2, n, for( j = 2, i, A[i, j] = A[i-1, j-1] + j * A[i-1, j] ) ); B = A^(-1); C = matrix( m, m, i, j, if( j == 1, 0^(i-1), sum( r = 0, i-j, B[i-j+1, r+1] * A[i-1+r, i-1] ) ) ); T = 1/C; }
%Y A360753 Cf. A132013, A215534, A354794, A354795, A360657 (matrix inverse).
%K A360753 sign,easy,tabl
%O A360753 0,5
%A A360753 _Werner Schulte_, Feb 21 2023