A357028
E.g.f. satisfies A(x) = (1 - x * A(x))^log(1 - x * A(x)).
Original entry on oeis.org
1, 0, 2, 6, 82, 820, 13568, 235368, 5111748, 123205248, 3404436312, 103998026880, 3516027852456, 129715202957184, 5198615642907360, 224652658604613120, 10419411912935774736, 516120552745366247424, 27198524267826237745824
Offset: 0
-
m = 20; (* number of terms *)
A[_] = 0;
Do[A[x_] = (1 - x*A[x])^Log[1 - x*A[x]] + 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)*abs(stirling(n, 2*k, 1))/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 *)
-
a(n) = sum(k=0, n\3, (3*k)!*(n+1)^(k-1)*abs(stirling(n, 3*k, 1))/(6^k*k!));
A357094
E.g.f. satisfies A(x)^A(x) = (1 - x * A(x))^(log(1 - x * A(x)) / 2).
Original entry on oeis.org
1, 0, 1, 3, 20, 170, 1789, 22869, 342222, 5874840, 113865786, 2459446440, 58588151148, 1526055579828, 43149414029604, 1316279791377810, 43090904609439900, 1506889769163738432, 56062825134853664328, 2211097753021838716116, 92149286987928381312972
Offset: 0
-
a(n) = sum(k=0, n\2, (2*k)!*(n-k+1)^(k-1)*abs(stirling(n, 2*k, 1))/(2^k*k!));
Showing 1-3 of 3 results.