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
-
a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*stirling(n, 3*k, 2)/k!);
A357037
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(log(1 - x * A(x))^2 / 6).
Original entry on oeis.org
1, 0, 0, 1, 6, 35, 295, 3304, 42112, 599724, 9657330, 174222576, 3464835726, 75208002792, 1771121398956, 44998593873024, 1226723273550720, 35714547582173280, 1106012915718532920, 36304411160854523520, 1259105580819317636280, 46007354360033491345920
Offset: 0
-
m = 22; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x])^(Log[1 - x*A[x]]^2/6) + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
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a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/(6^k*k!));
A357031
E.g.f. satisfies log(A(x)) = (exp(x * A(x)) - 1)^2 / 2.
Original entry on oeis.org
1, 0, 1, 3, 22, 195, 2131, 28623, 445789, 7982355, 161208976, 3626200743, 89942239861, 2438520508515, 71754865476841, 2277574224716703, 77570723071721938, 2821841221403098995, 109200125293424385271, 4479379126010806153143, 194148151869063307919725
Offset: 0
-
m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[(Exp[x*A[x]] - 1)^2/2] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
-
a(n) = sum(k=0, n\2, (2*k)!*(n+1)^(k-1)*stirling(n, 2*k, 2)/(2^k*k!));
Showing 1-3 of 3 results.