A368013 Expansion of e.g.f. 1/(1 - exp(x) + exp(2*x)).
1, -1, -1, 5, 11, -91, -301, 3485, 15371, -228811, -1261501, 22951565, 151846331, -3264973531, -25201039501, 625232757245, 5515342166891, -155079142742251, -1538993024478301, 48364005482108525, 533289474412481051, -18523127502677822971
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]=sum(j=1, i, (1-2^j)*binomial(i, j)*v[i-j+1])); v;
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PARI
my(x='x+O('x^30)); Vec(serlaplace(1/(1 - exp(x) + exp(2*x)))) \\ Joerg Arndt, Feb 10 2025
Formula
a(0) = 1; a(n) = Sum_{k=1..n} (1 - 2^k) * binomial(n,k) * a(n-k).