A377326
E.g.f. satisfies A(x) = 1 + (exp(x*A(x)) - 1)/A(x).
Original entry on oeis.org
1, 1, 1, 4, 15, 96, 665, 6028, 60907, 725560, 9591549, 142574004, 2323440119, 41519079616, 803667844993, 16797423268252, 376458083887875, 9014414549836296, 229564623594841637, 6197477089425914692, 176767174407208663759, 5312208220728020517136, 167760328500471584529321
Offset: 0
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terms=23; A[]=1; Do[A[x] = 1 + (Exp[x*A[x]] - 1)/A[x]+ O[x]^terms // Normal, terms]; CoefficientList[Series[A[x],{x,0,terms}],x]Range[0,terms-1]! (* Stefano Spezia, Aug 28 2025 *)
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a(n) = sum(k=0, (n+1)\2, (n-k)!/(n-2*k+1)!*stirling(n, k, 2));
A367163
E.g.f. satisfies A(x) = 1 + A(x)^3 * (exp(x*A(x)) - 1).
Original entry on oeis.org
1, 1, 9, 160, 4367, 161796, 7592593, 431826760, 28875060411, 2220199609420, 193010401410437, 18720726373805952, 2004328775014537111, 234797380878372574276, 29873926565253226992921, 4102473564838214815027576, 604804589755948599369229811
Offset: 0
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a(n) = sum(k=0, n, (n+3*k)!/(n+2*k+1)!*stirling(n, k, 2));
A377490
E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x*A(x)) - 1))^2.
Original entry on oeis.org
1, 2, 24, 560, 19844, 949632, 57398980, 4197775472, 360541351092, 35581415127200, 3968076446262116, 493536896206210320, 67738259336620421140, 10170114513821104697792, 1658107523049271429191492, 291735781263854493014688944, 55097256018925972909190946932
Offset: 0
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a(n) = 2*sum(k=0, n, (2*n+3*k+1)!/(2*n+2*k+2)!*stirling(n, k, 2));
A377495
E.g.f. satisfies A(x) = 1/(1 - A(x)^2 * (exp(x*A(x)^2) - 1)).
Original entry on oeis.org
1, 1, 11, 247, 8571, 404791, 24246439, 1761559647, 150540054611, 14798051914231, 1645040516034927, 204068062926942655, 27946847973073178587, 4188043229601371413911, 681707014005609312133175, 119774859918869807700934111, 22592863584958717501615734051, 4553853548371236985017395321335
Offset: 0
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a(n) = sum(k=0, n, (2*n+3*k)!/(2*n+2*k+1)!*stirling(n, k, 2));
A377498
E.g.f. satisfies A(x) = 1/(1 - A(x)^3 * (exp(x*A(x)^3) - 1)).
Original entry on oeis.org
1, 1, 15, 472, 23109, 1544236, 131066427, 13504084084, 1637471184585, 228472604080636, 36059751069011079, 6352095608437311844, 1235464848177560948685, 262972526121658780180300, 60804392657638382942192691, 15176441397584819546121452692, 4066926719970372629975938096017
Offset: 0
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a(n) = sum(k=0, n, (3*n+4*k)!/(3*n+3*k+1)!*stirling(n, k, 2));
A377491
E.g.f. satisfies A(x) = 1/(1 - A(x) * (exp(x*A(x)) - 1))^3.
Original entry on oeis.org
1, 3, 51, 1692, 85245, 5799348, 498288327, 51799641372, 6323803975545, 887056541576820, 140606281908386763, 24856199282033820396, 4848804928048309664181, 1034685331580238018659748, 239758404709207383049312239, 59955226332194712661373725884
Offset: 0
-
a(n) = 3*sum(k=0, n, (3*n+4*k+2)!/(3*n+3*k+3)!*stirling(n, k, 2));
Showing 1-6 of 6 results.