cp's OEIS Frontend

A347617 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) is the number of partitions of n^k into exactly n parts.

%I A347617 #15 Sep 09 2021 10:42:10
%S A347617 0,1,1,1,1,0,1,1,1,0,1,1,2,1,0,1,1,4,7,1,0,1,1,8,61,34,1,0,1,1,16,547,
%T A347617 1906,192,1,0,1,1,32,4921,117874,91606,1206,1,0,1,1,64,44287,7478386,
%U A347617 53830967,6023602,8033,1,0,1,1,128,398581,477568114,33219689231,43054503928,505853354,55974,1,0
%N A347617 Square array T(n,k), n >= 0, k >= 0, read by antidiagonals downwards, where T(n,k) is the number of partitions of n^k into exactly n parts.
%F A347617 T(n,k) = [x^(n^k-n)] Product_{j=1..n} 1/(1-x^j).
%e A347617 Square array begins:
%e A347617   0, 1,   1,     1,        1,           1, ...
%e A347617   1, 1,   1,     1,        1,           1, ...
%e A347617   0, 1,   2,     4,        8,          16, ...
%e A347617   0, 1,   7,    61,      547,        4921, ...
%e A347617   0, 1,  34,  1906,   117874,     7478386, ...
%e A347617   0, 1, 192, 91606, 53830967, 33219689231, ...
%o A347617 (PARI) T(n, k) = if(k==0, n==1, polcoef(prod(j=1, n, 1/(1-x^j+x*O(x^(n^k-n)))), n^k-n));
%Y A347617 Columns k=0..3 give A063524, A000012, A206240, A304176.
%Y A347617 Main diagonal gives A347606.
%Y A347617 Cf. A238016, A347615, A347618.
%K A347617 nonn,tabl
%O A347617 0,13
%A A347617 _Seiichi Manyama_, Sep 08 2021