A370934 Expansion of e.g.f. (1/x) * Series_Reversion( x*(4 - exp(3*x))/3 ).
1, 1, 7, 84, 1497, 35676, 1067931, 38548980, 1630600677, 79132611420, 4334891782095, 264625534657188, 17815224081030129, 1311349332273617196, 104778837463344022179, 9031998822763725245268, 835500403485829779202557, 82557790782397502710806396
Offset: 0
Keywords
Programs
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PARI
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(4-exp(3*x))/3)/x)) -
PARI
a(n) = sum(k=0, n, 3^(n-k)*(n+k)!*stirling(n, k, 2))/(n+1)!;
Formula
a(n) = (1/(n+1)!) * Sum_{k=0..n} 3^(n-k) * (n+k)! * Stirling2(n,k).