A371141
E.g.f. satisfies A(x) = 1 - x*A(x)^3 * log(1 - x).
Original entry on oeis.org
1, 0, 2, 3, 80, 390, 10764, 104160, 3162144, 48889008, 1647798480, 35939566080, 1347110453952, 38272507827840, 1593399505840128, 55860824012535360, 2575479834957911040, 107239963351030433280, 5453101063482843276288, 262319113586136087567360
Offset: 0
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a(n) = n!*sum(k=0, n\2, (3*k)!/(2*k+1)!*abs(stirling(n-k, k, 1))/(n-k)!);
A371142
E.g.f. satisfies A(x) = 1 + x*A(x)^2 * (exp(x) - 1).
Original entry on oeis.org
1, 0, 2, 3, 52, 245, 4446, 40327, 823432, 11539593, 269030530, 5151458411, 137198342700, 3328477618765, 100753779655270, 2948537330575215, 100684293424304656, 3437897124964763921, 131334298073705194506, 5110990692709364143219, 216634434142329948020020
Offset: 0
-
nmax = 20; CoefficientList[Series[(1 - Sqrt[1 + 4*x - 4*E^x*x]) / (2*(-x + E^x*x)), {x, 0, nmax}], x] * Range[0, nmax]! (* Vaclav Kotesovec, Mar 12 2024 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(2/(1+sqrt(1-4*x*(exp(x)-1)))))
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a(n) = n!*sum(k=0, n\2, (2*k)!/(k+1)!*stirling(n-k, k, 2)/(n-k)!);
A377438
E.g.f. satisfies A(x) = (1 - x * log(1 - x) * A(x))^2.
Original entry on oeis.org
1, 0, 4, 6, 136, 660, 13668, 128520, 2846240, 41368320, 1021615920, 20260896480, 564541372800, 14159468157120, 445236762450816, 13446791658256320, 474901138629918720, 16708336544212992000, 658279512232521209856, 26360704394322974161920, 1150065728368040063784960
Offset: 0
-
a(n) = 2*n!*sum(k=0, n\2, (2*k+1)!*abs(stirling(n-k, k, 1))/((n-k)!*(k+2)!));
Showing 1-3 of 3 results.