A383206 Triangle T(n,k), n >= 0, 0 <= k <= n, read by rows, where T(n,k) = Sum_{j=k..n} 2^(n-j) * Stirling2(n,j) * Stirling2(j,k).

1, 0, 1, 0, 3, 1, 0, 11, 9, 1, 0, 49, 71, 18, 1, 0, 257, 575, 245, 30, 1, 0, 1539, 4957, 3120, 625, 45, 1, 0, 10299, 45829, 39697, 11480, 1330, 63, 1, 0, 75905, 454015, 517790, 201677, 33250, 2506, 84, 1, 0, 609441, 4804191, 6999785, 3513762, 770007, 81774, 4326, 108, 1

Offset

0,5

Links

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

Formula

E.g.f. of column k (with leading zeros): (exp(f(x)) - 1)^k / k! with f(x) = (exp(2*x) - 1)/2.

Example

Triangle starts:
  1;
  0,     1;
  0,     3,     1;
  0,    11,     9,     1;
  0,    49,    71,    18,     1;
  0,   257,   575,   245,    30,    1;
  0,  1539,  4957,  3120,   625,   45,  1;
  0, 10299, 45829, 39697, 11480, 1330, 63, 1;
  ...

Prog

(PARI) T(n, k) = sum(j=k, n, 2^(n-j)*stirling(n, j, 2)*stirling(j, k, 2));

Crossrefs

Columns k=0..3 give A000007, A004211 (for n > 0), A383207, A383208.

Row sums give A380228.

Cf. A130191.

Sequence in context: A067176 A249480 A271704 * A307419 A383149 A256892

Adjacent sequences: A383203 A383204 A383205 * A383207 A383208 A383209

Keyword

nonn,tabl

Author

Seiichi Manyama, Apr 19 2025

Status

approved