A349559
E.g.f. satisfies A(x) = 1/(1 - x*A(x))^x.
Original entry on oeis.org
1, 0, 2, 3, 44, 270, 3714, 44940, 746528, 13149864, 271954440, 6154715160, 155055594792, 4254730262640, 127019898548256, 4088313657038520, 141301521555548160, 5216698433745207360, 204946906542573645504, 8536144551987171202560
Offset: 0
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a:= n-> n!*coeff(series(RootOf(1/(1-x*A)^x-A, A), x, n+1), x, n):
seq(a(n), n=0..20); # Alois P. Heinz, Nov 22 2021
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nmax = 20; A[] = 0; Do[A[x] = 1/(1 - x*A[x])^x + O[x]^(nmax + 1) // Normal, nmax + 1]; CoefficientList[A[x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Nov 22 2021 *)
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my(A=1,n=22); for(i=1, n, A=(1-x*A)^(-x+x*O(x^n))); Vec(serlaplace(A))
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a(n) = n!*sum(k=0, n\2, (n-k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!); \\ Seiichi Manyama, Aug 27 2022
A356786
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x * A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 92, 510, 15114, 174300, 5558944, 103712616, 3672530280, 96397602840, 3830335035240, 129817630491120, 5796134828193696, 239906921239210680, 11996259216566469120, 584024600798956215360, 32523678395272329425856
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n+k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A356796
E.g.f. satisfies A(x) = 1/(1 - x)^(x * A(x)^3).
Original entry on oeis.org
1, 0, 2, 3, 92, 450, 14454, 141540, 4980128, 78711696, 3048567480, 68677353360, 2930551701384, 86832573553440, 4079649847428960, 150444517302424800, 7768028697749806080, 342721736137376184960, 19392702029822685015360, 994397473912386435004800
Offset: 0
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a(n) = n!*sum(k=0, n\2, (3*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
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my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (3*k+1)^(k-1)*(-x*log(1-x))^k/k!)))
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(3*x*log(1-x))/3)))
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my(N=20, x='x+O('x^N)); Vec(serlaplace((lambertw(3*x*log(1-x))/(3*x*log(1-x)))^(1/3)))
A356884
E.g.f. satisfies A(x)^A(x) = 1/(1 - x*A(x))^x.
Original entry on oeis.org
1, 0, 2, 3, 20, 150, 1254, 14280, 190000, 2863728, 49465080, 954312480, 20303200488, 473604468480, 12007399511184, 328671680500800, 9663415159357440, 303695188102656000, 10159173955921651776, 360424299614544829440, 13517056067747847719040
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n-2*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A356885
E.g.f. satisfies A(x)^(A(x)^2) = 1/(1 - x*A(x))^x.
Original entry on oeis.org
1, 0, 2, 3, -4, 30, 954, 6300, 6432, 424872, 18273960, 260682840, 1754408424, 47063118960, 2314149100704, 54798086299320, 773632032345600, 20746972036284480, 1072205580591921600, 36098491880448944640, 816375193722964932480, 25160238159364392336000
Offset: 0
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a(n) = n!*sum(k=0, n\2, (n-3*k+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
Showing 1-5 of 5 results.