A348014 Triangle, read by rows, with row n forming the coefficients in Product_{k=0..n} (1 + k^k*x).

1, 1, 1, 1, 5, 4, 1, 32, 139, 108, 1, 288, 8331, 35692, 27648, 1, 3413, 908331, 26070067, 111565148, 86400000, 1, 50069, 160145259, 42405161203, 1216436611100, 5205269945088, 4031078400000

Offset

0,5

Links

Seiichi Manyama, Rows n = 0..37, flattened

Formula

T(0,0) = 1; T(n,k) = T(n-1,k) + n^n * T(n-1,k-1).

Example

Triangle begins:
  1;
  1,    1;
  1,    5,      4;
  1,   32,    139,      108;
  1,  288,   8331,    35692,     27648;
  1, 3413, 908331, 26070067, 111565148, 86400000;

Prog

(PARI) T(n, k) = if(k==0, 1, if(k==n, prod(j=1, n, j^j), T(n-1, k)+n^n*T(n-1, k-1)));
(PARI) row(n) = Vecrev(prod(k=1, n, 1+k^k*x));

Crossrefs

Column k=1 gives A001923.

The diagonal of the triangle is A002109.

Cf. A007318, A008955, A023531, A108084, A173007, A173008, A249677.

Sequence in context: A182824 A329120 A152862 * A108440 A102220 A279151

Adjacent sequences: A348011 A348012 A348013 * A348015 A348016 A348017

Keyword

nonn,tabl

Author

Seiichi Manyama, Sep 24 2021

Status

approved