A367152
E.g.f. satisfies A(x) = 1 - log(1 - x*A(x)^3).
Original entry on oeis.org
1, 1, 7, 101, 2250, 68184, 2619822, 122071704, 6689791392, 421670267136, 30055781201520, 2390512621714656, 209893714832795760, 20165895195283566000, 2104433775967024226592, 237043144515185017456320, 28664975599576485530851584, 3704019298858867019823244800
Offset: 0
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Table[(3*n)! * Sum[Abs[StirlingS1[n,k]]/(3*n-k+1)!, {k,0,n}], {n,0,20}] (* Vaclav Kotesovec, Nov 07 2023 *)
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a(n) = (3*n)!*sum(k=0, n, abs(stirling(n, k, 1))/(3*n-k+1)!);
A367078
E.g.f. satisfies A(x) = 1 + log(1 + x*A(x)^2).
Original entry on oeis.org
1, 1, 3, 14, 82, 514, 2508, -12328, -820752, -22232232, -498433320, -9865850688, -159373484448, -1136343398880, 65056426313760, 4663237803223680, 210535052582008320, 7821007002377349120, 242387957802121971840, 5333182310844833642496
Offset: 0
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a(n) = (2*n)!*sum(k=0, n, stirling(n, k, 1)/(2*n-k+1)!);
A367153
E.g.f. satisfies A(x) = 2 - exp(-x*A(x)^2).
Original entry on oeis.org
1, 1, 3, 13, 55, -59, -8869, -230019, -4735569, -81845819, -925266221, 11304277117, 1342388191079, 64570153427781, 2378028350945547, 68237841920780221, 1044508709568828511, -45901762542718407035, -5887687395597254917885, -396339747040666473203907
Offset: 0
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a(n) = (2*n)!*sum(k=0, n, (-1)^(n-k)*stirling(n, k, 2)/(2*n-k+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)));
A377360
E.g.f. satisfies A(x) = ( 1 - log(1 - x*A(x)) )^2.
Original entry on oeis.org
1, 2, 12, 130, 2082, 44488, 1192964, 38557860, 1459988440, 63414711072, 3108861424032, 169829819311392, 10230860299538400, 673850170929176928, 48176129912775680160, 3715759452364764485280, 307545698210584533055488, 27190399275422185989742080, 2557448587458299889542868480
Offset: 0
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nmax = 20; CoefficientList[1/x * InverseSeries[Series[x/(1 - Log[1 - x])^2, {x, 0, nmax + 1}], x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Aug 27 2025 *)
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a(n) = 2*(2*n+1)!*sum(k=0, n, abs(stirling(n, k, 1))/(2*n-k+2)!);
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 1-6 of 6 results.