A379868
E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^2) + x*A(x)^2.
Original entry on oeis.org
1, 0, 1, -1, 25, -101, 2281, -19895, 472305, -6760297, 177126121, -3578690435, 105341330953, -2743981145933, 91092111623241, -2888769295882111, 107832291781283809, -4009180998104138321, 167254334458983887689, -7105017992715364001147, 328862774630320838523321
Offset: 0
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
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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)!);
A379911
E.g.f. A(x) satisfies A(x) = exp(-x*A(x)^3) + x*A(x)^2.
Original entry on oeis.org
1, 0, 1, -4, 53, -656, 11917, -244896, 6080265, -171274240, 5480682041, -195121452032, 7672945614589, -329902678161408, 15405361461450885, -776248476561903616, 41985495698339969681, -2426188309657908936704, 149180887282915274036977, -9725086440331395237937152
Offset: 0
A379932
E.g.f. A(x) satisfies A(x) = ( exp(-x) + x*A(x) )^2.
Original entry on oeis.org
1, 0, 2, 10, 88, 978, 13468, 221338, 4233584, 92458018, 2271283684, 62012911530, 1863436238728, 61124896911154, 2173660174175228, 83304031307483962, 3423089366607304672, 150143469737701318722, 7001969736087834197716, 345972733119776006045386
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(4*exp(-2*x)/(1+sqrt(1-4*x*exp(-x)))^2))
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a(n) = -2*n!*sum(k=0, n, (-k-2)^(n-k-1)*binomial(2*k+1, k)/(n-k)!);
Showing 1-4 of 4 results.