cp's OEIS Frontend

A347621 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 distinct parts.

%I A347621 #18 Sep 09 2021 10:41:31
%S A347621 1,1,1,1,1,1,1,1,1,1,1,1,2,2,1,1,1,6,8,2,1,1,1,32,192,32,3,1,1,1,390,
%T A347621 84756,16444,142,4,1,1,1,16444,5807301632,11784471548,3207086,668,5,1,
%U A347621 1,1,4013544,2496696209705056142,16816734263788624008200,74443865946867656,1258238720,3264,6,1
%N A347621 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 distinct parts.
%F A347621 T(n,k) = A000009(n^k).
%e A347621 Square array begins:
%e A347621   1, 1,  1,     1,           1, ...
%e A347621   1, 1,  1,     1,           1, ...
%e A347621   1, 1,  2,     6,          32, ...
%e A347621   1, 2,  8,   192,       84756, ...
%e A347621   1, 2, 32, 16444, 11784471548, ...
%t A347621 Table[If[n == k == 0, 1, PartitionsQ[#^k] &[n - k]], {n, 0, 9}, {k, n, 0, -1}] // Flatten (* _Michael De Vlieger_, Sep 09 2021 *)
%o A347621 (PARI) T(n, k) = polcoef(prod(j=1, n^k, 1+x^j+x*O(x^(n^k))), n^k);
%Y A347621 Columns k=0..3 give A000012, A000009, A072243, A281501.
%Y A347621 Rows n=0+1, 2-3 give A000012, A067735, A070235.
%Y A347621 Main diagonal gives A064682.
%Y A347621 Cf. A347615, A347630.
%K A347621 nonn,tabl
%O A347621 0,13
%A A347621 _Seiichi Manyama_, Sep 09 2021