A383261 Expansion of e.g.f. f(x) * exp(2 * f(x)), where f(x) = (exp(3*x) - 1)/3.
0, 1, 7, 57, 527, 5441, 61959, 770281, 10364671, 149854545, 2313932471, 37963374329, 658873048623, 12050610195937, 231496456566631, 4657345160220681, 97873704021590111, 2143496712532350833, 48821033290172899095, 1154261436241093805593, 28279753601438144211343
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=1, n, k*2^(k-1)*3^(n-k)*stirling(n, k, 2));
Formula
a(n) = Sum_{k=1..n} k * 2^(k-1) * 3^(n-k) * Stirling2(n,k).