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A048801
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E.g.f. A(x) satisfies A(x) = 1 + x * A(exp(x) - 1).
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9
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1, 1, 2, 9, 64, 665, 9366, 170618, 3885120, 107728587, 3563482900, 138299564425, 6211739264688, 319190842232028, 18581124650376484, 1215078306042445710, 88602560159713837728, 7157866087368900148345, 636974235270930297047526
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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) = n * A213357(n-1) if n>0. a(n+1) = (n+1) * Sum_{k=0..n} a(k) * stirling2(n, k). - Michael Somos, Jun 11 2012
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EXAMPLE
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1 + x + 2*x^2 + 9*x^3 + 64*x^4 + 665*x^5 + 9366*x^6 + 170618*x^7 + 3885120*x^8 + ...
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MATHEMATICA
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nmax=20; b = ConstantArray[0, nmax+1]; b[[1]]=1; Do[b[[n+2]] = (n+1)*Sum[b[[k+1]]*StirlingS2[n, k], {k, 0, n}], {n, 0, 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 = 1 + x * subst( A, x, exp( x + A - A) - 1)); n! * polcoeff( A, n))} /* Michael Somos, Jun 11 2012 */
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CROSSREFS
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KEYWORD
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nonn,eigen
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AUTHOR
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EXTENSIONS
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STATUS
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approved
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