A385620 E.g.f. A(x) satisfies A(x) = exp( x*(A(2*x) + A(3*x)) ).
1, 2, 24, 1064, 158144, 78427712, 130391102464, 725657074158592, 13450842239318679552, 825492067428121929359360, 166724642619378284453845213184, 110175812687250637947409895640473600, 236918101449618886434191300434062010777600, 1649425480856495624442166311045759714226010423296
Offset: 0
Keywords
Programs
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Mathematica
terms = 14; A[] = 1; Do[A[x] =Exp[x*(A[2*x] + A[3*x])]+ O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Jul 05 2025 *)
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PARI
a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (j+1)*(2^j+3^j)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Formula
a(0) = 1; a(n) = Sum_{k=0..n-1} (k+1) * (2^k+3^k) * binomial(n-1,k) * a(k) * a(n-1-k).