A363008
Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(x) - 1) - 1) - 1)).
Original entry on oeis.org
1, 1, 6, 52, 594, 8444, 143783, 2854261, 64735570, 1651560175, 46814933977, 1459689346911, 49650414218071, 1829560770160335, 72603137881845927, 3086932915850946633, 139999909097319319787, 6746170002325663539844, 344199636595620793896784
Offset: 0
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b:= proc(n, m, t) option remember; `if`(n=0, `if`(t=1, m!,
b(m, 0, t-1)), m*b(n-1, m, t)+b(n-1, m+1, t))
end:
a:= n-> b(n, 0, 4):
seq(a(n), n=0..20); # Alois P. Heinz, May 12 2023
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(exp(exp(exp(x)-1)-1)-1))))
A363009
Expansion of e.g.f. 1/(2 - exp(exp(exp(exp(exp(x) - 1) - 1) - 1) - 1)).
Original entry on oeis.org
1, 1, 7, 71, 949, 15775, 313920, 7279795, 192828745, 5744627550, 190131836270, 6921735519110, 274885665920198, 11826225289547024, 547926995688877245, 27199542114163170649, 1440220170795372833970, 81026116511855753816058
Offset: 0
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b:= proc(n, m, t) option remember; `if`(n=0, `if`(t=1, m!,
b(m, 0, t-1)), m*b(n-1, m, t)+b(n-1, m+1, t))
end:
a:= n-> b(n, 0, 5):
seq(a(n), n=0..20); # Alois P. Heinz, May 12 2023
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(exp(exp(exp(exp(x)-1)-1)-1)-1))))
A099391
Expansion of e.g.f. 1/(2 - exp(exp(exp(x) - 1) - 1)).
Original entry on oeis.org
1, 1, 5, 36, 342, 4048, 57437, 950512, 17975438, 382424397, 9039989107, 235062317196, 6667866337309, 204905200542916, 6781157167505291, 240446179599065951, 9094120016963808935, 365453749501228063845
Offset: 0
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With[{nn=20},CoefficientList[Series[1/(2-Exp[Exp[Exp[x]-1]-1]),{x,0,nn}],x] Range[0,nn]!] (* Harvey P. Dale, Apr 10 2014 *)
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my(N=20, x='x+O('x^N)); Vec(serlaplace(1/(2-exp(exp(exp(x)-1)-1)))) \\ Seiichi Manyama, May 12 2023
A363010
a(n) = n! * [x^n] 1/(1 - f^n(x)), where f(x) = exp(x) - 1.
Original entry on oeis.org
1, 1, 4, 36, 594, 15775, 618838, 33757864, 2448904188, 228290728635, 26617527649365, 3797508644987398, 651082351708066303, 132130157056046918808, 31333332827346731906130, 8587011712002719806274022, 2693586800519167315881703732, 958983405298849163873718493941
Offset: 0
Main diagonal of
A153278 (for n>=1).
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b:= proc(n, t, m) option remember; `if`(n=0, `if`(t<2, m!,
b(m, t-1, 0)), m*b(n-1, t, m)+b(n-1, t, m+1))
end:
a:= n-> b(n$2, 0):
seq(a(n), n=0..20); # Alois P. Heinz, May 12 2023
Showing 1-4 of 4 results.