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A350200 Array read by antidiagonals: T(n,k) is the determinant of the Hankel matrix of the 2*n-1 consecutive primes starting at the k-th prime, n >= 0, k >= 1.

%I A350200 #9 Aug 25 2022 16:22:45
%S A350200 1,1,2,1,3,1,1,5,-4,-2,1,7,6,12,0,1,11,-30,-72,144,288,1,13,18,72,0,
%T A350200 576,-1728,1,17,-42,-72,288,1152,-7104,-26240,1,19,30,-96,144,-1248,
%U A350200 -11712,45248,222272,1,23,22,-188,488,-112,-11360,21184,450432,1636864
%N A350200 Array read by antidiagonals: T(n,k) is the determinant of the Hankel matrix of the 2*n-1 consecutive primes starting at the k-th prime, n >= 0, k >= 1.
%H A350200 Wikipedia, <a href="https://en.wikipedia.org/wiki/Hankel_matrix">Hankel matrix</a>
%e A350200 Array begins:
%e A350200   n\k|      1      2       3       4       5       6       7       8
%e A350200   ---+--------------------------------------------------------------
%e A350200    0 |      1      1       1       1       1       1       1       1
%e A350200    1 |      2      3       5       7      11      13      17      19
%e A350200    2 |      1     -4       6     -30      18     -42      30      22
%e A350200    3 |     -2     12     -72      72     -72     -96    -188    -480
%e A350200    4 |      0    144       0     288     144     488    1800    2280
%e A350200    5 |    288    576    1152   -1248    -112    4432   -1552   15952
%e A350200    6 |  -1728  -7104  -11712  -11360  -10816   29952  -89152  -57088
%e A350200    7 | -26240  45248   21184 -103168  -43264 -605440 -379264  271552
%e A350200    8 | 222272 450432 1068800 2022912 3927552 5399552 6315904 6861312
%e A350200 T(3,2) = 12, the determinant of the Hankel matrix
%e A350200   [3  5  7]
%e A350200   [5  7 11]
%e A350200   [7 11 13].
%o A350200 (Python)
%o A350200 from sympy import Matrix,prime,nextprime
%o A350200 def A350200(n,k):
%o A350200     p = [prime(k)] if n > 0 else []
%o A350200     for i in range(2*n-2): p.append(nextprime(p[-1]))
%o A350200     return Matrix(n,n,lambda i,j:p[i+j]).det()
%Y A350200 Cf. A350201.
%Y A350200 Cf. A000012 (row n = 0), A000040 (row n = 1), A056221 (row n = 2 with opposite sign), A024356 (column k = 1), A071543 (column k = 2).
%K A350200 sign,tabl
%O A350200 0,3
%A A350200 _Pontus von Brömssen_, Dec 19 2021
%E A350200 Offset corrected by _Pontus von Brömssen_, Aug 25 2022