A356970
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^2 * A(x)).
Original entry on oeis.org
1, 0, 0, 6, 12, 40, 1980, 16128, 136080, 4224960, 70943040, 1087178400, 31274100000, 784834652160, 18115033128192, 565994928945600, 18161466717139200, 560655551681971200, 20108422243585658880, 769928646324249699840, 29464638272901949824000
Offset: 0
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m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x])^(x^2*A[x]) + 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) = n!*sum(k=0, n\3, (n-k+1)^(k-1)*abs(stirling(n-2*k, k, 1))/(n-2*k)!);
A356971
E.g.f. satisfies A(x) = 1/(1 - x * A(x))^(x^3 * A(x)).
Original entry on oeis.org
1, 0, 0, 0, 24, 60, 240, 1260, 108864, 1149120, 12160800, 138045600, 5605649280, 122049607680, 2378318604480, 45712559692800, 1529842399303680, 47673689320857600, 1382823169839820800, 38831806109898547200, 1378613101427645184000
Offset: 0
-
m = 21; (* number of terms *)
A[_] = 0;
Do[A[x_] = 1/(1 - x*A[x])^(x^3*A[x]) + 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) = n!*sum(k=0, n\4, (n-2*k+1)^(k-1)*abs(stirling(n-3*k, k, 1))/(n-3*k)!);
A371146
E.g.f. satisfies A(x) = 1/(1 - x*A(x)^2)^(x*A(x)^2).
Original entry on oeis.org
1, 0, 2, 3, 116, 690, 24714, 315840, 11919088, 250812072, 10389272040, 310700914920, 14351129171400, 557402214180240, 28831564284582864, 1372162923004025880, 79345973798740154880, 4450055092134985771200, 286324089075857021558976
Offset: 0
-
a(n) = n!*sum(k=0, n\2, (2*n+1)^(k-1)*abs(stirling(n-k, k, 1))/(n-k)!);
A376350
E.g.f. satisfies A(x) = 1/(1 - x^2*A(x)^2)^(x*A(x)).
Original entry on oeis.org
1, 0, 0, 6, 0, 60, 2520, 1680, 181440, 6138720, 18295200, 1444988160, 46443196800, 357015859200, 25016537145600, 818965321574400, 12259854032025600, 815066633667686400, 28461465853402982400, 691667282863484928000, 45198900807076912896000, 1739192274792359202816000, 60318174486002275287244800
Offset: 0
-
my(N=30, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2)^x)/x))
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a(n) = n!*sum(k=0, n\2, (n+1)^(n-2*k-1)*abs(stirling(k, n-2*k, 1))/k!);