A347667 Triangle read by rows: T(n,k) = Sum_{j=0..k} binomial(n,j) * j! (0 <= k <= n).

1, 1, 2, 1, 3, 5, 1, 4, 10, 16, 1, 5, 17, 41, 65, 1, 6, 26, 86, 206, 326, 1, 7, 37, 157, 517, 1237, 1957, 1, 8, 50, 260, 1100, 3620, 8660, 13700, 1, 9, 65, 401, 2081, 8801, 28961, 69281, 109601, 1, 10, 82, 586, 3610, 18730, 79210, 260650, 623530, 986410

Offset

0,3

Links

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

Example

Triangle begins:
  1;
  1, 2;
  1, 3,  5;
  1, 4, 10,  16;
  1, 5, 17,  41,   65;
  1, 6, 26,  86,  206,  326;
  1, 7, 37, 157,  517, 1237, 1957;
  1, 8, 50, 260, 1100, 3620, 8660, 13700;
  ...

Mathematica

T[n_, k_] := Sum[Binomial[n, j] j!, {j, 0, k}]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten

Crossrefs

T(n,n) = A000522, T(2*n,n) = A066211.

Cf. A008279, A008949, A111063, A121662, A285268.

Sequence in context: A210557 A118243 A210233 * A297582 A134081 A134247

Adjacent sequences: A347664 A347665 A347666 * A347668 A347669 A347670

Keyword

nonn,tabl

Author

Ilya Gutkovskiy, Sep 10 2021

Status

approved