A368763 a(n) = n! * (1 + Sum_{k=0..n} binomial(k+2,3) / k!).
1, 2, 8, 34, 156, 815, 4946, 34706, 277768, 2500077, 25000990, 275011176, 3300134476, 42901748643, 600624481562, 9009367224110, 144149875586576, 2450547884972761, 44109861929510838, 838087376660707252, 16761747533214146580, 351996698197497079951
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace((1+x*sum(k=0, 2, binomial(2, k)*x^k/(k+1)!)*exp(x))/(1-x)))
Formula
a(0) = 1; a(n) = n*a(n-1) + binomial(n+2,3).
a(n) = n! + A368574(n).
E.g.f.: (1 + x * (1+x+x^2/6) * exp(x)) / (1-x).