A379871
E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^3) + x*A(x)^3.
Original entry on oeis.org
1, 0, 1, -1, 37, -151, 5041, -45277, 1548457, -23466079, 857700181, -18904086037, 752753527021, -21985835786383, 961877988836857, -34996151990315341, 1686330291491184337, -73237182836313686719, 3882675760305075969949, -195288563442324161608165
Offset: 0
A379877
E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x*A(x)^3.
Original entry on oeis.org
1, 0, 1, 2, 33, 244, 4345, 61830, 1332961, 28087208, 739562481, 20380504330, 644853623425, 21767589641628, 810480865644073, 32246095869576974, 1385625666085792065, 63366863108725330000, 3090966367543869021409, 159607809547688836085778, 8718178798812199357657441
Offset: 0
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Table[-n! * Sum[(-2*n - 1)^(n-k-1) * Binomial[2*n + k, k]/(n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 15 2025 *)
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a(n) = -n!*sum(k=0, n, (-2*n-1)^(n-k-1)*binomial(2*n+k, k)/(n-k)!);
A379876
E.g.f. A(x) satisfies A(x) = exp(-x*A(x)) + x*A(x)^3.
Original entry on oeis.org
1, 0, 1, 5, 53, 689, 11509, 231083, 5448841, 147483665, 4508952641, 153682778435, 5778729641629, 237643665397241, 10610714800698349, 511207317411929339, 26434273616510818961, 1460296693254659368481, 85832214445015447832569, 5348490494660467991798003
Offset: 0
A379879
E.g.f. A(x) satisfies A(x) = exp(-x) + x*A(x)^2.
Original entry on oeis.org
1, 0, 1, 5, 41, 439, 5869, 94275, 1770705, 38102255, 924580181, 24984120523, 744154938361, 24224671103463, 855748556756157, 32604902612628419, 1332864500919743393, 58192519232324179423, 2702582455278623736997, 133037424985668849756603
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(2*exp(-x)/(1+sqrt(1-4*x*exp(-x)))))
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a(n) = -n!*sum(k=0, n, (-k-1)^(n-k-1)*binomial(2*k, k)/(n-k)!);
Showing 1-4 of 4 results.