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
Examples
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; ...
Crossrefs
Programs
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PARI
T(n, k) = sum(j=k, n, 2^(n-j)*stirling(n, j, 2)*stirling(j, k, 2));
Formula
E.g.f. of column k (with leading zeros): (exp(f(x)) - 1)^k / k! with f(x) = (exp(2*x) - 1)/2.