A356962
E.g.f. satisfies log(A(x)) = x^2/2 * (exp(x*A(x)) - 1) * A(x).
Original entry on oeis.org
1, 0, 0, 3, 6, 10, 465, 3801, 20608, 461196, 7609185, 85446955, 1661943756, 38070386718, 692342989429, 15023805426735, 404978989779120, 10131679290423736, 264474729910772433, 8059571860456028835, 249785940327179846500, 7837578968934515202570
Offset: 0
-
a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*stirling(n-2*k, k, 2)/(2^k*(n-2*k)!));
A356968
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^3/6 * A(x)).
Original entry on oeis.org
1, 0, 0, 0, 4, 10, 40, 210, 4144, 40320, 409800, 4527600, 72552480, 1170449280, 19489513680, 338983444800, 6672681818880, 141166715289600, 3149324442700800, 73497460049395200, 1825098639493104000, 47984287767342796800, 1326460667797094860800
Offset: 0
-
a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*abs(stirling(n-3*k, k, 1))/(6^k*(n-3*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)!);
Showing 1-3 of 3 results.