A367840 Expansion of e.g.f. 1/(2 + x - exp(4*x)).
1, 3, 34, 514, 10456, 265704, 8103120, 288302480, 11722944896, 536262671488, 27256865214208, 1523936708699904, 92949383868668928, 6141694449341637632, 437033351625771001856, 33319937543640487708672, 2709708041047388536274944
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, 4^j*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = -n * a(n-1) + Sum_{k=1..n} 4^k * binomial(n,k) * a(n-k).