A285381
G.f.: 1/(1 - 1!*x/(1 - 2!*x^2/(1 - 3!*x^3/(1 - 4!*x^4/(1 - 5!*x^5/(1 - 6!*x^6/(1 - ...))))))), a continued fraction.
Original entry on oeis.org
1, 1, 1, 3, 5, 11, 33, 67, 169, 435, 1265, 3035, 8025, 22243, 60721, 191307, 491657, 1404371, 4089633, 12183835, 36872377, 126189219, 350136977, 1062359147, 3386475177, 10757830387, 36121721857, 120817807419, 482847966617, 1391650703939, 4654331013489
Offset: 0
G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 5*x^4 + 11*x^5 + 33*x^6 + 67*x^7 + 169*x^8 + ...
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nmax = 30; CoefficientList[Series[1/(1 + ContinuedFractionK[-k! x^k, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
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a(n) = my(A=1+O(x)); for(i=1, n, A=1-(n-i+1)!*x^(n-i+1)/A); polcoef(1/A, n); \\ Seiichi Manyama, Apr 16 2021
A343428
G.f.: 1 + 1!*x/(1 + 2!*x/(1 + 3!*x/(1 + 4!*x/(1 + 5!*x/(1 + ...))))).
Original entry on oeis.org
1, 1, -2, 16, -416, 47104, -31623680, 151868796928, -5929687248674816, 2103645975156790263808, -7506342628191723555983065088, 295743482602620866090259230372134912, -140189608695401234244797733914829257462251520, 865523452956329002149153403380412177220307414830546944
Offset: 0
A307084
Expansion of 1/(1 - 1^1*x/(1 - 2^2*x/(1 - 3^3*x/(1 - 4^4*x/(1 - 5^5*x/(1 - ...)))))), a continued fraction.
Original entry on oeis.org
1, 1, 5, 133, 31769, 95375641, 4353388262525, 3536446917781244413, 58773633134246903294470769, 22612364832863674279489837434733681, 224919094724957152626614652086970769074005045, 63900685361274641827300282511815586348785532532913331893
Offset: 0
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nmax = 11; CoefficientList[Series[1/(1 + ContinuedFractionK[-k^k x, 1, {k, 1, nmax}]), {x, 0, nmax}], x]
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a(n) = my(A=1+O(x)); for(i=1, n, A=1-(n-i+1)^(n-i+1)*x/A); polcoef(1/A, n); \\ Seiichi Manyama, Apr 15 2021
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