A355094 E.g.f. A(x) satisfies A(x) = 1 + 3 * (1 - exp(-x)) * A(1 - exp(-x)).
1, 3, 15, 84, 321, -2157, -57126, -23496, 19229199, 114026754, -14369595177, -124727102772, 21679898019936, 89714147328354, -57010454409251982, 653678598376462566, 223463102168891738085, -9691395708350731626375, -1087655068021435814109648
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]=3*sum(j=1, i, (-1)^(i-j)*j*stirling(i, j, 2)*v[j])); v;
Formula
E.g.f. A(x) satisfies: A(-log(1-x)) = 1 + 3*x*A(x).
a(0) = 1; a(n) = 3 * Sum_{k=1..n} (-1)^(n-k) * k * Stirling2(n,k) * a(k-1).