A386504 E.g.f. A(x) satisfies A(x) = exp(x + x^6*A'''''(x)).
1, 1, 1, 1, 1, 1, 721, 3638881, 73388931841, 4439222967191041, 671254901566891891201, 223293614016982999277652481, 148555455012284806644741491166721, 183545166980276574090600617506568885761, 396856587856894056179855967245699021196188161, 1430118352830649099320069857966516939680956145171201
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]=v[i]+sum(j=0, i-1, (1+j)*sum(k=1, 5, stirling(5, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
a(0) = 1; a(n) = a(n-1) + Sum_{k=0..n-1} (1 + k) * (24*k - 50*k^2 + 35*k^3 - 10*k^4 + k^5) * binomial(n-1,k) * a(k) * a(n-1-k).
a(n) == 1 (mod 720). - Hugo Pfoertner, Jul 24 2025