A357345
E.g.f. satisfies A(x) = -log(1 - x * exp(A(x))) * exp(3 * A(x)).
Original entry on oeis.org
0, 1, 9, 173, 5226, 216564, 11429592, 733443990, 55447217928, 4826605609584, 475490102407200, 52299789903627408, 6353202640983827472, 844774875973448667792, 122040471544637793494760, 19034141943046836097099080, 3187643959565686909679931648
Offset: 0
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a(n) = sum(k=1, n, (n+3*k)^(k-1)*abs(stirling(n, k, 1)));
A357333
E.g.f. satisfies A(x) = -log(1 - x) * exp(2 * A(x)).
Original entry on oeis.org
0, 1, 5, 50, 778, 16604, 451668, 14947568, 582982160, 26187136128, 1331445995520, 75589772147328, 4739901861071232, 325353447339098112, 24264683011603485696, 1953776475810372817920, 168924939633683095452672, 15609228287753846217412608
Offset: 0
-
nmax = 17; A[_] = 0;
Do[A[x_] = -Log[1 - x]*Exp[2*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 05 2024 *)
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(2*log(1-x))/2)))
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a(n) = sum(k=1, n, (2*k)^(k-1)*abs(stirling(n, k, 1)));
A357322
Expansion of e.g.f. -LambertW(log(1 - 3*x)/3).
Original entry on oeis.org
0, 1, 5, 45, 586, 10024, 213084, 5428072, 161475320, 5501761488, 211466328400, 9057714349672, 428022643010544, 22127292215218072, 1242503403120434168, 75319473068729478360, 4902798528238919060224, 341102498012848479889408
Offset: 0
-
With[{m = 20}, Range[0, m]! * CoefficientList[Series[-ProductLog[Log[1 - 3*x]/3], {x, 0, m}], x]] (* Amiram Eldar, Sep 24 2022 *)
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my(N=20, x='x+O('x^N)); concat(0, Vec(serlaplace(-lambertw(log(1-3*x)/3))))
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a(n) = sum(k=1, n, 3^(n-k)*k^(k-1)*abs(stirling(n, k, 1)));
A357393
E.g.f. satisfies A(x) = -log(1 - x * exp(3 * A(x))).
Original entry on oeis.org
0, 1, 7, 110, 2730, 93024, 4037880, 213127200, 13253058000, 948964262400, 76899763100160, 6957624460550400, 695236239163065600, 76043127767523840000, 9036546669251861760000, 1159342449440429270016000, 159708538424128885551360000, 23512778013219939149561856000
Offset: 0
-
a(n) = sum(k=1, n, (3*n)^(k-1)*abs(stirling(n, k, 1)));
-
a(n) = sum(k=1, n, (4*n)^(k-1)*stirling(n, k, 1));
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a(n) = if(n==0, 0, (4*n-1)!/(3*n)!);
Showing 1-4 of 4 results.