A367838 Expansion of e.g.f. 1/(2 + x - exp(2*x)).
1, 1, 6, 38, 344, 3832, 51408, 803952, 14371456, 289005440, 6457624832, 158719896832, 4255775425536, 123619815742464, 3867071262472192, 129610289219999744, 4633674344869756928, 176011269522607144960, 7079115958438736363520
Offset: 0
Keywords
Programs
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=-i*v[i]+sum(j=1, i, 2^j*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = -n * a(n-1) + Sum_{k=1..n} 2^k * binomial(n,k) * a(n-k).