A380647
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-3*x)/(1 + x)^3 ).
Original entry on oeis.org
1, 6, 105, 3246, 146637, 8780688, 657224901, 59140486800, 6223651526457, 750357182131200, 102014741343847329, 15443915464974191616, 2576937457466957107845, 469914373917914931984384, 92982800086882512621716925, 19843243096453465663599962112, 4543276116844426827394718716401
Offset: 0
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nmax=17; CoefficientList[(1/x)InverseSeries[Series[x*Exp[-3*x]/(1 + x)^3 ,{x,0,nmax}]],x]Range[0,nmax-1]! (* Stefano Spezia, Feb 06 2025 *)
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a(n) = 3*n!*sum(k=0, n, (3*n+3)^(k-1)*binomial(3*n+3, 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!);
A380945
Expansion of e.g.f. (1/x) * Series_Reversion( x * (1 - x)^2 * exp(-2*x) ).
Original entry on oeis.org
1, 4, 50, 1124, 37192, 1637232, 90278176, 5992556320, 465599728512, 41470892979200, 4167168740195584, 466428111222196224, 57556315795242096640, 7763511917730857967616, 1136484206117494859980800, 179453678311835212416585728, 30404317385796994658988752896
Offset: 0
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a(n, q=2, r=2, s=2, 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.