A354613 Expansion of e.g.f. 1/(2 - (1 + x)^x).
1, 0, 2, -3, 44, -210, 2694, -23520, 330672, -4168584, 67622040, -1095648840, 20621674776, -403514963280, 8734659594192, -199049377658040, 4894304369356800, -126907901533425600, 3501394314254828352, -101643840316833194880, 3112491474764866339200
Offset: 0
Keywords
Programs
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PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(2-(1+x)^x))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j!*sum(k=0, j\2, stirling(j-k, k, 1)/(j-k)!)*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} A007113(k) * binomial(n,k) * a(n-k).