A357084
E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^2 * A(x).
Original entry on oeis.org
1, 0, 2, 6, 98, 990, 19082, 347046, 8512226, 220737390, 6776521082, 225532370646, 8413133799314, 339965749171230, 14995100013227882, 711308930246853126, 36278600375671552322, 1974411768891211652430, 114394542828023045764442
Offset: 0
-
a(n) = sum(k=0, n\2, (2*k)!*(n+k+1)^(k-1)*stirling(n, 2*k, 2)/k!);
A357085
E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1)^3 * A(x).
Original entry on oeis.org
1, 0, 0, 6, 36, 150, 3780, 77406, 1059156, 21669990, 640319940, 16622025486, 450085011156, 15416323450710, 561938117029380, 20587443165165246, 835816881563118036, 37282225483118856390, 1722621978491064495300, 83817942806509377794286
Offset: 0
-
a(n) = sum(k=0, n\3, (3*k)!*(n+k+1)^(k-1)*stirling(n, 3*k, 2)/k!);
A367201
E.g.f. satisfies log(A(x)) = (exp(x*A(x)) - 1) * A(x)^3.
Original entry on oeis.org
1, 1, 10, 200, 6167, 258607, 13748744, 886397829, 67211684890, 5861684458896, 578088714806497, 63617223837958309, 7728596914020856162, 1027393177458209939977, 148344954037140113652010, 23119776330887635387231580, 3868359765874829925197165527
Offset: 0
-
a(n) = sum(k=0, n, (n+3*k+1)^(k-1)*stirling(n, k, 2));
A355508
E.g.f. satisfies log(A(x)) = x^2 * (exp(x * A(x)) - 1) * A(x).
Original entry on oeis.org
1, 0, 0, 6, 12, 20, 1830, 15162, 82376, 3326472, 59467050, 678585710, 20553790092, 563969783676, 10776243950654, 318310813941330, 10988438698692240, 303144002003606672, 9910024990673571666, 392381835437286982998, 14072003919511407720020
Offset: 0
-
m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[x^2*(Exp[x*A[x]] - 1)*A[x]] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m - 1]! (* Jean-François Alcover, Sep 12 2022 *)
-
a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*stirling(n-2*k, k, 2)/(n-2*k)!);
A356892
E.g.f. satisfies log(A(x)) = x^3 * (exp(x * A(x)) - 1) * A(x).
Original entry on oeis.org
1, 0, 0, 0, 24, 60, 120, 210, 101136, 1089144, 7409520, 39917790, 4097460840, 100410712116, 1474154203704, 16356956618730, 786764261166240, 30867868254267120, 778327514455987296, 14658714575197061814, 522720977799308061240, 25075479032600008569900
Offset: 0
-
m = 22; (* number of terms *)
A[_] = 0;
Do[A[x_] = Exp[x^3*(Exp[x*A[x]] - 1)*A[x]] + O[x]^m // Normal, {m}];
CoefficientList[A[x], x]*Range[0, m-1]! (* Jean-François Alcover, Sep 12 2022 *)
-
a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*stirling(n-3*k, k, 2)/(n-3*k)!);