A385547 E.g.f. A(x) satisfies A(x) = Sum_{k>=0} x^k/k! * A(k^2*x).
1, 1, 3, 22, 413, 18656, 2030287, 513423436, 300561564025, 398653905380896, 1192260459720446171, 7941386767782184832204, 117226647607145106003271333, 3808187092459275036716509871776, 271053748414379190468548152694690551, 42093494971632722160142716694680694172956
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Keywords
Programs
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Mathematica
a[0] = 1; a[n_] := a[n] = Sum[Binomial[n,k] * (n-k)^(2*k) * a[k], {k, 0, n-1}]; Table[a[n], {n, 0, 20}] (* Vaclav Kotesovec, Jul 03 2025 *) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (i-j)^(2*j)*binomial(i, j)*v[j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=0..n-1} (n-k)^(2*k) * binomial(n,k) * a(k).