A048801
E.g.f. A(x) satisfies A(x) = 1 + x * A(exp(x) - 1).
Original entry on oeis.org
1, 1, 2, 9, 64, 665, 9366, 170618, 3885120, 107728587, 3563482900, 138299564425, 6211739264688, 319190842232028, 18581124650376484, 1215078306042445710, 88602560159713837728, 7157866087368900148345, 636974235270930297047526
Offset: 0
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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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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{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 */
A354728
E.g.f. A(x) satisfies A(x) = 1 + log(1+x) * A(log(1+x)).
Original entry on oeis.org
1, 1, 1, -1, -6, 39, 97, -4481, 33912, 676236, -26413226, 238849819, 14313503696, -755420105545, 10108190752293, 933595772081187, -74703766573019512, 1828010869875477868, 148132864489851652128, -19789393233722946227592, 910780967051245532791008
Offset: 0
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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, 1)*v[j])); v;
A353177
E.g.f. A(x) satisfies A(x) = 1 + (1 - exp(-x)) * A(1 - exp(-x)).
Original entry on oeis.org
1, 1, 1, -2, -13, 61, 612, -8924, -41991, 2821876, -22689807, -1196339088, 45175812442, 10968806278, -63633205318330, 2495113782094766, 31372553334367367, -8832192422722410665, 421480840601004167822, 9536361803340658184343
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, (-1)^(i-j)*j*stirling(i, j, 2)*v[j])); v;
A355083
E.g.f. A(x) satisfies A(x) = 1 + 2 * (exp(x) - 1) * A(exp(x) - 1).
Original entry on oeis.org
1, 2, 10, 86, 1106, 19562, 451014, 13051586, 460907034, 19434738686, 961628831658, 55046140338642, 3602414472002206, 266842000568643866, 22180625837341816898, 2053584526860808500094, 210393497508897167616290, 23715128208081620773251530
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=2*sum(j=1, i, j*stirling(i, j, 2)*v[j])); v;
A355092
E.g.f. A(x) satisfies A(x) = 1 + 3 * (exp(x) - 1) * A(exp(x) - 1).
Original entry on oeis.org
1, 3, 21, 246, 4215, 97743, 2917200, 108150780, 4850518269, 257827235520, 15978078982389, 1139042647968096, 92364503720316726, 8439008013526902906, 861692986696232539398, 97635567184812702273234, 12199893866233489801453323, 1671886886212411035295719261
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=3*sum(j=1, i, j*stirling(i, j, 2)*v[j])); v;
A355122
E.g.f. A(x) satisfies A(x) = 1 + (exp(x) - 1) * A(2 * (exp(x) - 1)).
Original entry on oeis.org
1, 1, 5, 73, 2725, 242921, 50068197, 23441365641, 24644653272869, 57655911504114985, 297771560486880287589, 3370400630994211122517705, 83052841013576647141181337509, 4428866659075152490151174819022697, 508340576698412171558866359984025695205
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*2^(j-1)*stirling(i, j, 2)*v[j])); v;
Showing 1-6 of 6 results.