A358081
Expansion of e.g.f. 1/(1 - x^3 * exp(x)).
Original entry on oeis.org
1, 0, 0, 6, 24, 60, 840, 10290, 80976, 847224, 13306320, 190271070, 2677088040, 46082426676, 874515884424, 16582066303530, 336875275380000, 7539189088358640, 176554878235711776, 4295134487197296054, 111114287924643309240, 3036073975138066955820
Offset: 0
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With[{nn=30},CoefficientList[Series[1/(1-x^3 Exp[x]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Aug 12 2025 *)
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my(N=30, x='x+O('x^N)); Vec(serlaplace(1/(1-x^3*exp(x))))
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a(n) = n!*sum(k=0, n\3, k^(n-3*k)/(n-3*k)!);
A370984
Expansion of e.g.f. (1/x) * Series_Reversion( x*(1 - x^2*exp(x)) ).
Original entry on oeis.org
1, 0, 2, 6, 84, 860, 14430, 257082, 5678456, 140241096, 3952791450, 123539438990, 4266378769092, 160943793753756, 6592371152535350, 291260465060881890, 13809548247503299440, 699362685890810753552, 37679514498664685654706
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(serreverse(x*(1-x^2*exp(x)))/x))
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a(n) = sum(k=0, n\2, k^(n-2*k)*(n+k)!/(k!*(n-2*k)!))/(n+1);
A366459
Expansion of e.g.f. -log(1 - x^2 * exp(x)).
Original entry on oeis.org
0, 0, 2, 6, 24, 140, 990, 8442, 84056, 955656, 12227130, 173812430, 2717859012, 46362339036, 856770362630, 17050946225250, 363576478312560, 8269357341437072, 199837364514425586, 5113346326011170838, 138106722548779770620, 3926456810081828991780
Offset: 0
A375629
Expansion of e.g.f. exp(2*x) / (1 - x^2 * exp(x)).
Original entry on oeis.org
1, 2, 6, 26, 148, 1052, 8974, 89294, 1015480, 12991832, 184682554, 2887850858, 49261993444, 910356170804, 18117379906630, 386315966673638, 8786555389140976, 212335975835710256, 5433155029435593970, 146744457899073450050, 4172032796528725318876
Offset: 0
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my(N=30, x='x+O('x^N)); Vec(serlaplace(exp(2*x)/(1-x^2*exp(x))))
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a(n) = n!*sum(k=0, n\2, (k+2)^(n-2*k)/(n-2*k)!);
A377532
Expansion of e.g.f. 1/(1 - x^2 * exp(x))^3.
Original entry on oeis.org
1, 0, 6, 18, 180, 1500, 15930, 191646, 2580648, 38683224, 636068430, 11392350090, 220658360076, 4594593295188, 102333126352002, 2427278515815510, 61079333377870800, 1625065147997303856, 45576552142354413078, 1343802083242003570818, 41552482139458105525620
Offset: 0
A377531
Expansion of e.g.f. 1/(1 - x^2 * exp(x))^2.
Original entry on oeis.org
1, 0, 4, 12, 96, 760, 7260, 80724, 1008112, 14079888, 216881460, 3652767580, 66773963784, 1316433381432, 27840054610732, 628626642921060, 15093709672205280, 383989133237230624, 10317497504580922212, 291958800400148127660, 8678485827979443326200
Offset: 0
Showing 1-6 of 6 results.