A353186 Expansion of e.g.f. 1/(1 - Sum_{k>=1} d(k) * x^k / k), where d(n) = number of divisors of n (A000005).
1, 1, 4, 22, 170, 1588, 18236, 240840, 3662424, 62456136, 1185150768, 24714979584, 562659843984, 13870798275072, 368324715871680, 10478253239415552, 317975367247809408, 10252138622419702656, 349999438215928660992, 12612365665457524786944, 478414908509124826439424
Offset: 0
Keywords
Programs
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Mathematica
d[k_] := d[k] = DivisorSigma[0, k]; a[0] = 1; a[n_] := a[n] = Sum[(k - 1)! * d[k] * Binomial[n, k] * a[n - k], {k, 1, n}]; Array[a, 21, 0] (* Amiram Eldar, Apr 30 2022 *) -
PARI
my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-sum(k=1, N, numdiv(k)*x^k/k)))) -
PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (j-1)!*numdiv(j)*binomial(i, j)*v[i-j+1])); v;
Formula
a(0) = 1; a(n) = Sum_{k=1..n} A318249(k) * binomial(n,k) * a(n-k).