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A213357
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E.g.f. satisfies A(x) = 1 + (exp(x) - 1) * A(exp(x) - 1).
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7
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1, 1, 3, 16, 133, 1561, 24374, 485640, 11969843, 356348290, 12572687675, 517644938724, 24553141710156, 1327223189312606, 81005220402829714, 5537660009982114858, 421050946315817655785, 35387457515051683169307, 3269500807582223015227780
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) = Sum_{k=1..n} k * a(k-1) * Stirling2(n, k) if n>0.
A048801(n) = n * a(n-1) = Sum_{k=1..n} a(k) * Stirling1(n, k) if n>0.
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EXAMPLE
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1 + x + 3*x^2 + 16*x^3 + 133*x^4 + 1561*x^5 + 24374*x^6 + 485640*x^7 + ...
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MATHEMATICA
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nmax=20; b = ConstantArray[0, nmax+1]; b[[1]]=1; Do[b[[n+1]] = Sum[k*b[[k]]*StirlingS2[n, k], {k, 1, n}], {n, 1, nmax-1}]; b (* Vaclav Kotesovec, Mar 12 2014 *)
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PROG
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(PARI) {a(n) = local(A); if( n<0, 0, A = 1 + O(x); for( k=1, n, A = subst( 1 + x * A, x, exp( x + x * (A - A)) - 1)); n! * polcoeff( A, n))}
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*stirling(i, j, 2)*v[j])); v; \\ Seiichi Manyama, Jun 04 2022
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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