A380723
E.g.f. A(x) satisfies A(x) = exp(x * A(x)^2) / (1 - x*A(x)^2).
Original entry on oeis.org
1, 2, 21, 436, 13785, 589206, 31825381, 2080523880, 159761186577, 14097898530730, 1405926737063541, 156379679761925148, 19195200442017128425, 2577494115099820986174, 375845854490491567916805, 59145488004443221188738256, 9990898494797767848442559649, 1803160967691789114062089511250
Offset: 0
A360609
E.g.f. satisfies A(x) = exp(x*A(x)^3) / (1-x).
Original entry on oeis.org
1, 2, 17, 313, 9053, 357941, 17975605, 1095604133, 78570635225, 6482415935449, 604889610870881, 62989604872166897, 7241672622495518773, 911048848278644776949, 124497704904842673086285, 18364053909500922198147421, 2908158473059042016441887025
Offset: 0
A370875
Expansion of e.g.f. (1/x) * Series_Reversion( x/(x + exp(x^2)) ).
Original entry on oeis.org
1, 1, 4, 24, 228, 2820, 44400, 840000, 18669840, 475871760, 13698296640, 439402803840, 15545690233920, 601352177025600, 25251437978807040, 1143932660001331200, 55612090342967558400, 2887929114414030086400, 159548423949650274739200
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x/(x+exp(x^2)))/x))
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a(n) = n!*sum(k=0, n\2, (2*k+1)^(k-1)*binomial(n, 2*k)/k!);
A371040
E.g.f. satisfies A(x) = exp(x^3*A(x)^2) / (1-x).
Original entry on oeis.org
1, 1, 2, 12, 96, 840, 9720, 143640, 2399040, 45239040, 976752000, 23537606400, 621444700800, 17936155036800, 562855739846400, 19038932398886400, 690456599575142400, 26748823900403404800, 1102407824344284057600, 48147134965603914240000
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(sqrt(lambertw(-2*x^3/(1-x)^2)/(-2*x^3))))
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a(n) = n!*sum(k=0, n\3, (2*k+1)^(k-1)*binomial(n-k, n-3*k)/k!);
Showing 1-4 of 4 results.