A386503 E.g.f. A(x) satisfies A(x) = exp(x + x^5*A''''(x)).
1, 1, 1, 1, 1, 121, 87841, 221971681, 1493423016961, 22593988839985921, 683468095232158346881, 37898988106295372711276161, 3602374572375663444650415755521, 556397556871212729711470761587498241, 133676738300734051631377763872501373230081, 48173754506706929414138973409107160269088573441
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, 4, stirling(4, 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) * (-6*k + 11*k^2 - 6*k^3 + k^4) * binomial(n-1,k) * a(k) * a(n-1-k).
a(n) == 1 (mod 120). - Hugo Pfoertner, Jul 24 2025