A055883 Exponential transform of Pascal's triangle A007318.

1, 1, 1, 2, 4, 2, 5, 15, 15, 5, 15, 60, 90, 60, 15, 52, 260, 520, 520, 260, 52, 203, 1218, 3045, 4060, 3045, 1218, 203, 877, 6139, 18417, 30695, 30695, 18417, 6139, 877, 4140, 33120, 115920, 231840, 289800, 231840, 115920, 33120, 4140, 21147

Offset: 0

Author

Christian G. Bower, Jun 09 2000

Keywords

• nonn
• tabl

Comments

Triangle T(n,k), 0 <= k <= n, read by rows, given by [1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, ...] DELTA [1, 1, 1, 2, 1, 3, 1, 4, 1, 5, 1, 6, ...] where DELTA is the operator defined in A084938. - Philippe Deléham, Aug 10 2005

Examples

			   1;
   1,  1;
   2,  4,  2;
   5, 15, 15,  5;
  15, 60, 90, 60, 15;
  ...
		

Links

• N. J. A. Sloane, Transforms
• Index entries for triangles and arrays related to Pascal's triangle

Crossrefs

Cf. A000110, A007318, A056860.

Row sums give A055882.

Programs

Mathematica

T[ n_, k_] := Binomial[n, k] * BellB[n]; (* Michael Somos, Apr 09 2025 *)

PARI

T(n, k) = binomial(n, k) * sum(j=0, n, stirling(n, j, 2)); /* Michael Somos, Apr 09 2025 */

Formula

a(n,k) = Bell(n)*C(n,k).

E.g.f.: A(x,y) = exp(exp(x+xy)-1).