A383262 Expansion of e.g.f. f(x)^2 * exp(f(x)) / 2, where f(x) = (exp(3*x) - 1)/3.
0, 0, 1, 12, 123, 1270, 13776, 158718, 1944685, 25294338, 348340491, 5064749074, 77528735868, 1246096312188, 20976610875949, 368984700979440, 6767792258171547, 129182459141936566, 2561529454871582772, 52676675861728386114, 1121762199908797394977
Offset: 0
Keywords
Programs
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PARI
a(n) = sum(k=2, n, 3^(n-k)*binomial(k, 2)*stirling(n, k, 2));
Formula
a(n) = Sum_{k=2..n} 3^(n-k) * binomial(k,2) * Stirling2(n,k).