A379933
Expansion of e.g.f. 1/( exp(-x) - x )^2.
Original entry on oeis.org
1, 4, 22, 158, 1408, 15002, 186100, 2634998, 41937136, 741170834, 14402727484, 305225470046, 7005711916840, 173134991854970, 4583675648417044, 129424786945875398, 3882446011526729440, 123304773913531035170, 4133369745467043807340, 145840627118145774415214
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x)^2))
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a(n) = n!*sum(k=0, n, (k+1)*(k+2)^(n-k)/(n-k)!);
A379942
Expansion of e.g.f. 1/( exp(-x) - x )^3.
Original entry on oeis.org
1, 6, 45, 411, 4449, 55803, 796581, 12757503, 226588257, 4420898595, 94001021589, 2163619250895, 53598352999905, 1421924243354787, 40221778417553637, 1208471542554184767, 38434396264371831873, 1289995362325669726659, 45567027291743788320405
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(exp(-x)-x)^3))
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a(n) = n!*sum(k=0, n, (k+3)^(n-k)*binomial(k+2, 2)/(n-k)!);
A379993
Expansion of e.g.f. 1/(1 - x * exp(x))^4.
Original entry on oeis.org
1, 4, 28, 252, 2776, 35940, 533304, 8908228, 165247072, 3368072196, 74782987240, 1796037420804, 46379441090448, 1281203788073092, 37694510810334616, 1176606639075726660, 38833052393329645504, 1351066066253778043908, 49417629820950190273992
Offset: 0
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nmax=18;CoefficientList[Series[1/(1 - x * Exp[x])^4,{x,0,nmax}],x]Range[0,nmax]! (* Stefano Spezia, Feb 05 2025 *)
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a(n) = n!*sum(k=0, n, k^(n-k)*binomial(k+3, 3)/(n-k)!);
A379994
Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^4.
Original entry on oeis.org
1, 5, 37, 349, 3969, 52641, 796069, 13502693, 253667297, 5225690017, 117090480021, 2834363683317, 73697918467105, 2048252470006913, 60587779740857573, 1900347489736371301, 62992469337321611073, 2200238756416513719489, 80765631192992760237205
Offset: 0
A379995
Expansion of e.g.f. exp(-2*x)/(exp(-x) - x)^4.
Original entry on oeis.org
1, 6, 48, 476, 5608, 76372, 1179016, 20332580, 387225120, 8068825988, 182564048824, 4456476380644, 116724944900272, 3264981100202564, 97130013288324552, 3062011655207131748, 101963095705628194624, 3576126056313566090500, 131762871920106615643480
Offset: 0
A379996
Expansion of e.g.f. exp(-x)/(exp(-x) - x)^4.
Original entry on oeis.org
1, 7, 61, 639, 7825, 109683, 1731645, 30403495, 587595649, 12395233539, 283385424829, 6979650164391, 184235963026833, 5188528445210035, 155284012799863453, 4921569063327156807, 164672737994453759617, 5800532536265417597571, 214559605389429001486557
Offset: 0
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With[{nn=20},CoefficientList[Series[Exp[-x]/(Exp[-x]-x)^4,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, May 19 2025 *)
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a(n) = n!*sum(k=0, n, (k+3)^(n-k)*binomial(k+3, 3)/(n-k)!);
Showing 1-6 of 6 results.