A380646
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-2*x)/(1 + x)^2 ).
Original entry on oeis.org
1, 4, 46, 932, 27568, 1080432, 52916176, 3115326496, 214470890496, 16914853191680, 1504252282653184, 148956086481767424, 16256865070022066176, 1938988214539948730368, 250943399365390735104000, 35026523834624205803491328, 5245178283068781060488298496, 838841884254236846183525646336
Offset: 0
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nmax=18; CoefficientList[(1/x)InverseSeries[Series[x*Exp[-2*x]/(1 + x)^2 ,{x,0,nmax}]],x]Range[0,nmax-1]! (* Stefano Spezia, Feb 06 2025 *)
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a(n) = 2*n!*sum(k=0, n, (2*n+2)^(k-1)*binomial(2*n+2, n-k)/k!);
A380648
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-4*x)/(1 + x)^4 ).
Original entry on oeis.org
1, 8, 188, 7816, 475096, 38289504, 3857806144, 467330651456, 66209818738176, 10747317030192640, 1967261819870112256, 400989528160028255232, 90087157573721153554432, 22119056538323287540637696, 5893098619063477612068864000, 1693364632974231188010697990144
Offset: 0
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nmax=16; CoefficientList[(1/x)InverseSeries[Series[x*Exp[-4*x]/(1 + x)^4, {x, 0, nmax}]], x]Range[0, nmax-1]! (* Stefano Spezia, Feb 06 2025 *)
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a(n) = 4*n!*sum(k=0, n, (4*n+4)^(k-1)*binomial(4*n+4, n-k)/k!);
A380946
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^3 * exp(-3*x) ).
Original entry on oeis.org
1, 6, 111, 3678, 179073, 11588688, 938905551, 91542271824, 10444685410881, 1365936450693120, 201503447217869679, 33108736185915906816, 5997057218957213126721, 1187319940110958086623232, 255104922613608981003351375, 59120580081196768991316314112
Offset: 0
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a(n, q=3, r=3, s=3, t=0, u=1) = q*n!*sum(k=0, n, (r*n+(s-r)*k+q)^(k-1)*binomial((r*u+1)*n+((s-r)*u+t-1)*k+q*u-1, n-k)/k!);
Showing 1-3 of 3 results.