A357025
E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^3.
Original entry on oeis.org
1, 0, 0, 6, 36, 150, 3060, 62286, 867636, 15591750, 419764500, 10834588446, 277719263316, 8580282719190, 297021183388020, 10459810717672686, 393932179466738676, 16351788886638987750, 717798906181149294420, 32905220431196072057406
Offset: 0
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a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*stirling(n, 3*k, 2)/k!);
A357009
E.g.f. satisfies log(A(x)) = (exp(x) - 1)^2 * A(x).
Original entry on oeis.org
1, 0, 2, 6, 50, 390, 4322, 53046, 782210, 12920550, 241747682, 5000171286, 113961184130, 2830240421190, 76196913418082, 2209152734071926, 68655746019566210, 2276606079902438310, 80244521295497399522, 2995966456305973559766, 118119901491333724203650
Offset: 0
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nmax = 20; A[_] = 1;
Do[A[x_] = Exp[(-1 + Exp[x])^2*A[x]] + O[x]^(nmax+1) // Normal, {nmax}];
CoefficientList[A[x], x]*Range[0, nmax]! (* Jean-François Alcover, Mar 04 2024 *)
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a(n) = sum(k=0, n\2, (2*k)!*(k+1)^(k-1)*stirling(n, 2*k, 2)/k!);
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my(N=30, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k+1)^(k-1)*(exp(x)-1)^(2*k)/k!)))
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(-lambertw(-(exp(x)-1)^2))))
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my(N=30, x='x+O('x^N)); Vec(serlaplace(-lambertw(-(exp(x)-1)^2)/(exp(x)-1)^2))
Showing 1-2 of 2 results.