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
-
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)!);
A379878
E.g.f. A(x) satisfies A(x) = exp(-x) + x*A(x)^3.
Original entry on oeis.org
1, 0, 1, 8, 97, 1544, 30673, 732752, 20486401, 656713520, 23755416481, 957430990328, 42552022022497, 2067669370359800, 109058922249721585, 6205740584180119424, 378947624701223801089, 24718152376534891564256, 1715322065909959400535361, 126186162087426817989206888
Offset: 0
-
Table[-n! * Sum[(-2*k-1)^(n-k-1) * Binomial[3*k, k] / (n-k)!, {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Jan 23 2025 *)
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a(n) = -n!*sum(k=0, n, (-2*k-1)^(n-k-1)*binomial(3*k, k)/(n-k)!);
A379875
E.g.f. A(x) satisfies A(x) = exp(-x*A(x)) + x.
Original entry on oeis.org
1, 0, 1, -4, 29, -256, 2797, -36352, 549145, -9468928, 183661721, -3960254464, 94011364405, -2436944723968, 68503370394565, -2075866971897856, 67464214813124273, -2340885649895194624, 86377064031382020913, -3377541983440381935616, 139515670016074334382541
Offset: 0
Showing 1-4 of 4 results.