A367134
E.g.f. satisfies A(x) = 1/(2 - exp(x*A(x)^2)).
Original entry on oeis.org
1, 1, 7, 97, 2051, 58681, 2122695, 92960001, 4782826459, 282821367001, 18901822316543, 1409070858589153, 115925274671836371, 10433564954705754681, 1019782291631652745591, 107570331041074850633473, 12180277895590328004331019, 1473587743517654702900335705
Offset: 0
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Table[1/(2*n+1)! * Sum[(2*n+k)! * StirlingS2[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
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a(n) = sum(k=0, n, (2*n+k)!*stirling(n, k, 2))/(2*n+1)!;
A367139
E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^3)).
Original entry on oeis.org
1, 1, 9, 167, 4780, 186004, 9173780, 548563140, 38573633016, 3119384230176, 285237426927552, 29102185296785160, 3277703460197645232, 403931173342682581296, 54066960915411480743520, 7811249803193620134996864, 1211525560869437165319590400
Offset: 0
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Table[1/(3*n+1)! * Sum[(3*n+k)! * Abs[StirlingS1[n,k]], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
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a(n) = sum(k=0, n, (3*n+k)!*abs(stirling(n, k, 1)))/(3*n+1)!;
A376392
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 + log(1-x))^2 ).
Original entry on oeis.org
1, 2, 16, 238, 5270, 156048, 5803980, 260301564, 13679476864, 824735208864, 56125075306656, 4256136846770400, 355933078611032880, 32544591173495688480, 3230049230183020829184, 345849932418702558032736, 39738632934736396340588160, 4877326190739889592547393792
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1+log(1-x))^2)/x))
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a(n) = 2*sum(k=0, n, (2*n+k+1)!*abs(stirling(n, k, 1)))/(2*n+2)!;
A367136
E.g.f. satisfies A(x) = 1/(1 - log(1 + x*A(x)^2)).
Original entry on oeis.org
1, 1, 5, 50, 764, 15804, 413426, 13094864, 487323000, 20844584760, 1007739144312, 54343954158240, 3234285062655984, 210581685526690464, 14889759832273000320, 1136236597054802033664, 93074880409847175490560, 8146156595011083708521472
Offset: 0
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Table[1/(2*n+1)! * Sum[(2*n+k)! * StirlingS1[n,k], {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
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a(n) = sum(k=0, n, (2*n+k)!*stirling(n, k, 1))/(2*n+1)!;
A377349
E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^2)/A(x)^2.
Original entry on oeis.org
1, 1, 1, 8, 62, 744, 11102, 201704, 4323720, 106591584, 2974873656, 92674125840, 3188299718496, 120053825169888, 4911082489042992, 216879763758962688, 10283600782413709056, 521088305671611058176, 28101278301136842204288, 1606968565080853531472640
Offset: 0
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a(n) = sum(k=0, (2*n+1)\3, (2*n-2*k)!/(2*n-3*k+1)!*abs(stirling(n, k, 1)));
A377426
E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^4)).
Original entry on oeis.org
1, 1, 11, 254, 9096, 443874, 27487034, 2065181880, 182545878152, 18562391987880, 2134764133508832, 273978733525211472, 38820518588599921200, 6019219063397716575840, 1013766602891962529642832, 184300120562198063868474624, 35971439241165448281366023424
Offset: 0
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a(n) = sum(k=0, n, (4*n+k)!*abs(stirling(n, k, 1)))/(4*n+1)!;
A371297
E.g.f. satisfies A(x) = 1/(1 + 2*log(1 - x*A(x)^2)).
Original entry on oeis.org
1, 2, 26, 676, 26852, 1443888, 98183024, 8083614880, 781958648448, 86940057459840, 10925288128027968, 1531414930604605440, 236905910564035082112, 40093453025252047368192, 7368774639911257328778240, 1461607086204159742139338752, 311206233406111454756938844160
Offset: 0
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a(n) = sum(k=0, n, 2^k*(2*n+k)!*abs(stirling(n, k, 1)))/(2*n+1)!;
A377329
E.g.f. satisfies A(x) = 1 - A(x)^2 * log(1 - x*A(x)^2).
Original entry on oeis.org
1, 1, 9, 164, 4590, 174364, 8388634, 489088592, 33523741560, 2642134225416, 235430782725744, 23405320602599616, 2568397523286868080, 308376740778642665856, 40213392368801846121792, 5659917793199595766848000, 855188706536492203489860480, 138068648223418996408877210496
Offset: 0
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a(n) = sum(k=0, n, (2*n+2*k)!/(2*n+k+1)!*abs(stirling(n, k, 1)));
Showing 1-8 of 8 results.