A367181
E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x)^2.
Original entry on oeis.org
1, 1, 3, 22, 261, 4186, 85035, 2096242, 60793257, 2028053146, 76512294567, 3221179205410, 149713378082301, 7614267616582810, 420634056602820099, 25081994054279063506, 1605673188973569254481, 109838361160586478627226, 7995918540574019507985471
Offset: 0
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a(n) = sum(k=0, n, (3*n-2*k)!/(3*n-3*k+1)!*stirling(n, k, 2));
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
-
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));
A377324
E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^3) - 1)/A(x).
Original entry on oeis.org
1, 1, 5, 52, 839, 18436, 513797, 17366224, 690366875, 31565619916, 1632064968929, 94159057903384, 5996889060457055, 417920884113926740, 31634205840603000221, 2584579552124805784672, 226699825143636127509347, 21247444370267806167804316, 2119206766514801966851437113
Offset: 0
-
a(n) = sum(k=0, n, (3*n-k)!/(3*n-2*k+1)!*stirling(n, k, 2));
A366729
E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2)/A(x).
Original entry on oeis.org
1, 1, 1, -4, -36, 14, 3100, 22112, -374640, -9520320, 9674808, 4085208192, 55207595520, -1640647901088, -69445046214336, 103240707929088, 71686341699216384, 1439635203885275136, -60449514895261440000, -3608840044036879934976
Offset: 0
-
a(n) = sum(k=0, n, (2*n-k)!/(2*n-2*k+1)!*stirling(n, k, 1));
A377347
E.g.f. satisfies A(x) = 1 + (exp(x*A(x)^2) - 1)/A(x)^2.
Original entry on oeis.org
1, 1, 1, 7, 41, 391, 4509, 62847, 1038001, 19580071, 418681877, 9973993855, 262293996777, 7545559829991, 235715629493005, 7946944965054271, 287592204406672481, 11120005819664145895, 457514133092462477253, 19957535405566629526335, 920056233384401619083545
Offset: 0
-
a(n) = sum(k=0, (2*n+1)\3, (2*n-2*k)!/(2*n-3*k+1)!*stirling(n, k, 2));
A377330
E.g.f. satisfies A(x) = 1 + A(x)^2 * (exp(x*A(x)^2) - 1).
Original entry on oeis.org
1, 1, 9, 163, 4537, 171451, 8206517, 476071275, 32469361617, 2546397256651, 225784275815485, 22336278201427675, 2439097416667718297, 291422424985108052091, 37817207428965579915333, 5296739332085114983427083, 796419825874139713780172449, 127955324543685857975407200235
Offset: 0
-
a(n) = sum(k=0, n, (2*n+2*k)!/(2*n+k+1)!*stirling(n, k, 2));
Showing 1-6 of 6 results.