A356963
E.g.f. satisfies log(A(x)) = x^3/6 * (exp(x*A(x)) - 1) * A(x).
Original entry on oeis.org
1, 0, 0, 0, 4, 10, 20, 35, 2856, 30324, 205920, 1108965, 23266540, 482882686, 6894708184, 75981906455, 1191424314640, 28555511625320, 635370500529216, 11547272842560969, 213976417787571540, 5165550420447656050, 142251473243071866520, 3624660458114853235771
Offset: 0
-
a(n) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*stirling(n-3*k, k, 2)/(6^k*(n-3*k)!));
A356967
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^2/2 * A(x)).
Original entry on oeis.org
1, 0, 0, 3, 6, 20, 540, 4284, 35700, 698760, 10591560, 155024100, 3231336240, 68704908480, 1451024062488, 35843008924800, 950925111973200, 25881184257364800, 765471782499860160, 24210772652940214320, 797021694060934204800, 27752674398657594805440
Offset: 0
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a(n) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*abs(stirling(n-2*k, k, 1))/(2^k*(n-2*k)!));
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)!);
Showing 1-3 of 3 results.