A347615 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.

1, 1, 1, 1, 1, 1, 1, 1, 2, 1, 1, 1, 5, 3, 1, 1, 1, 22, 30, 5, 1, 1, 1, 231, 3010, 231, 7, 1, 1, 1, 8349, 18004327, 1741630, 1958, 11, 1, 1, 1, 1741630, 133978259344888, 365749566870782, 3163127352, 17977, 15, 1, 1, 1, 4351078600, 233202632378520643600875145, 61847822068260244309086870983975, 1606903190858354689128371, 15285151248481, 173525, 22, 1

Offset

0,9

Links

Table of n, a(n) for n=0..54.

Formula

T(n,k) = A000041(n^k).

Example

Square array begins:
  1, 1,   1,       1,               1, ...
  1, 1,   1,       1,               1, ...
  1, 2,   5,      22,             231, ...
  1, 3,  30,    3010,        18004327, ...
  1, 5, 231, 1741630, 365749566870782, ...

Prog

(PARI) T(n, k) = numbpart(n^k);

Crossrefs

Columns k=0..3 give A000012, A000041, A072213, A128854.

Rows n=0+1, 2-10 give A000012, A068413, A248728, A068413(2*n), A248730, A248732, A248734, A068413(3*n), A248728(2*n), A070177.

Main diagonal gives A347607.

Cf. A238016, A347617, A347618, A347621.

Sequence in context: A256384 A111673 A121391 * A241194 A352893 A008326

Adjacent sequences: A347612 A347613 A347614 * A347616 A347617 A347618

Keyword

nonn,tabl

Author

Seiichi Manyama, Sep 08 2021

Status

approved