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)!;
A367138
E.g.f. satisfies A(x) = 1/(1 + log(1 - x*A(x)^2)).
Original entry on oeis.org
1, 1, 7, 98, 2096, 60684, 2221766, 98488592, 5129567208, 307066395000, 20775900638472, 1567955813868960, 130596146677118448, 11899839375083061024, 1177540373453616858240, 125754589311488009416704, 14416305655742615673941760, 1765794816084642802179333120
Offset: 0
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Table[1/(2*n+1)! * Sum[(2*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, (2*n+k)!*abs(stirling(n, k, 1)))/(2*n+1)!;
A367137
E.g.f. satisfies A(x) = 1/(1 - log(1 + x*A(x)^3)).
Original entry on oeis.org
1, 1, 7, 101, 2248, 68024, 2608940, 121316796, 6633841608, 417181294704, 29665022908992, 2353675598751960, 206145540193974288, 19755830347828845360, 2056381966404400741920, 231034314706671715165824, 27865886237401381188422400, 3591366670194210901813749120
Offset: 0
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Table[1/(3*n+1)! * Sum[(3*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, (3*n+k)!*stirling(n, k, 1))/(3*n+1)!;
Showing 1-3 of 3 results.