A217033
Expansion of e.g.f. 1/(1 - log(1 - log(1-x))).
Original entry on oeis.org
1, 1, 2, 7, 33, 198, 1432, 12136, 117772, 1287718, 15658052, 209568126, 3061140398, 48454548452, 826155841924, 15094511153752, 294206836405288, 6093273074402848, 133628182522968752, 3093469935389714928, 75384936371166307872, 1928960833317580172688
Offset: 0
E.g.f.: A(x) = 1 + x + 2*x^2/2! + 7*x^3/3! + 33*x^4/4! + 198*x^5/5! +...
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CoefficientList[Series[1/(1-Log[1-Log[1-x]]), {x, 0, 20}], x]* Range[0, 20]! (* Vaclav Kotesovec, Feb 12 2013 *)
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{a(n)=n!*polcoeff(1/(1-log(1-log(1-x +x*O(x^n)))),n)}
for(n=0,25,print1(a(n),", "))
A305988
Expansion of e.g.f. 1/(1 + log(2 - exp(x))).
Original entry on oeis.org
1, 1, 4, 24, 194, 1970, 24062, 343294, 5601122, 102847794, 2098766582, 47117285270, 1154031484586, 30622256174458, 875092190716382, 26794239236959806, 875110094707912562, 30367988674208286914, 1115822099409002188358, 43276913813553367194598, 1766830322476935945014330
Offset: 0
1/(1 + log(2 - exp(x))) = 1 + x + 4*x^2/2! + 24*x^3/3! + 194*x^4/4! + 1970*x^5/5! + 24062*x^6/6! + ...
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b:= proc(n) b(n):= n!*`if`(n=0, 1, add(b(k)/(k!*(n-k)), k=0..n-1)) end:
a:= n-> add(Stirling2(n, j)*b(j$2), j=0..n):
seq(a(n), n=0..25); # Alois P. Heinz, Jun 15 2018
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nmax = 20; CoefficientList[Series[1/(1 + Log[2 - Exp[x]]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Sum[StirlingS2[n, k] Abs[StirlingS1[k, j]] j!, {j, 0, k}], {k, 0, n}], {n, 0, 20}]
A306037
Expansion of e.g.f. 1/(1 + log(1 - log(1 + x))).
Original entry on oeis.org
1, 1, 2, 7, 31, 178, 1200, 9588, 86592, 887086, 10035164, 125472246, 1705102394, 25175822644, 399387494956, 6801042408728, 123348694663480, 2379855020533664, 48569042602254128, 1047134236970183664, 23748242269316806752, 565834452464428045872, 14117321495269290091440
Offset: 0
1/(1 + log(1 - log(1 + x))) = 1 + x + 2*x^2/2! + 7*x^3/3! + 31*x^4/4! + 178*x^5/5! + 1200*x^6/6! + ...
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a:=series(1/(1+log(1-log(1+x))),x=0,23): seq(n!*coeff(a,x,n),n=0..22); # Paolo P. Lava, Mar 26 2019
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nmax = 22; CoefficientList[Series[1/(1 + Log[1 - Log[1 + x]]), {x, 0, nmax}], x] Range[0, nmax]!
Table[Sum[Sum[StirlingS1[n, k] Abs[StirlingS1[k, j]] j!, {j, 0, k}], {k, 0, n}], {n, 0, 22}]
a[0] = 1; a[n_] := a[n] = Sum[Sum[(j - 1)! StirlingS1[k, j], {j, 1, k}] a[n - k]/k!, {k, 1, n}]; Table[n! a[n], {n, 0, 22}]
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