A380035
E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*exp(x*A(x)) ).
Original entry on oeis.org
1, 1, 5, 42, 517, 8420, 171201, 4181128, 119339081, 3900501648, 143703797725, 5893732487456, 266358266633229, 13153210420876864, 704697559381904921, 40714369264722337920, 2523456287242464370321, 167019778198736205721856, 11757749450929277192860725
Offset: 0
A380043
E.g.f. A(x) satisfies A(x) = 1/( 1 - 3*x*exp(x*A(x)^3) )^(1/3).
Original entry on oeis.org
1, 1, 6, 73, 1364, 34585, 1110406, 43200535, 1975744856, 103892750209, 6176282882570, 409635957376591, 29988473838531748, 2402004132488328433, 208956515057627326094, 19619264794744128427495, 1977503574407863125008816, 212975277029523353673126529, 24408338689788753822318157330
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace((serreverse(x/(1+3*x*exp(x)))/x)^(1/3)))
-
a(n) = n!*sum(k=0, n, 3^k*k^(n-k)*binomial(n+1/3, k)/(n-k)!)/(3*n+1);
A380095
E.g.f. A(x) satisfies A(x) = 1/sqrt( 1 - 2*x*A(x)^2*exp(x*A(x)^2) ).
Original entry on oeis.org
1, 1, 9, 156, 4129, 147880, 6696591, 367141306, 23648581713, 1750754472840, 146492770433095, 13672570280741086, 1408330043282040825, 158697952371711709060, 19420527592823261136519, 2564857285665551372127570, 363619232307437704055993761, 55079007956127598819416831088
Offset: 0
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