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

0,4

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

Links

Table of n, a(n) for n=0..45.

N. J. A. Sloane, Transforms

Index entries for triangles and arrays related to Pascal's triangle

Formula

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

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

Example

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

Mathematica

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

Prog

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

Crossrefs

Cf. A000110, A007318, A056860.

Row sums give A055882.

Sequence in context: A268740 A120493 A085880 * A366588 A085843 A198715

Adjacent sequences: A055880 A055881 A055882 * A055884 A055885 A055886

Keyword

nonn,tabl

Author

Christian G. Bower, Jun 09 2000

Status

approved