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)!);
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)!);
A379992
Expansion of e.g.f. exp(-3*x)/(exp(-x) - x)^2.
Original entry on oeis.org
1, 1, 7, 41, 349, 3539, 42451, 585605, 9130297, 158692679, 3041499871, 63712004729, 1447946191957, 35479218963083, 932326476195115, 26153289728300909, 779995883104560241, 24644267406802467215, 822278654588440803511, 28891372907012629446881
Offset: 0
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With[{nn=20},CoefficientList[Series[Exp[-3x]/(Exp[-x]-x)^2,{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Jun 14 2025 *)
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a(n) = n!*sum(k=0, n, (k+1)*(k-1)^(n-k)/(n-k)!);
Showing 1-4 of 4 results.