OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..450
FORMULA
E.g.f.: exp(Sum_{k>=1} (-1)^(k+1)*(exp(x^k) - 1)/k).
E.g.f.: Product_{k>=1} B(x^k)^((-1)^(k+1)/k), where B(x) = exp(exp(x) - 1) = e.g.f. of Bell numbers (A000110).
EXAMPLE
E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 2*x^4/4! + x^5/5! + 77*x^6/6! + ... = (1 + x) * (1 + x^2)^(1/2!) * (1 + x^3)^(1/3!) * (1 + x^4)^(1/4!) * ...
MAPLE
a:=series(exp(add((-1)^(k+1)*(exp(x^k)-1)/k, k=1..100)), x=0, 24): seq(n!*coeff(a, x, n), n=0..23); # Paolo P. Lava, Mar 26 2019
MATHEMATICA
nmax = 23; CoefficientList[Series[Exp[Sum[(-1)^(k + 1) (Exp[x^k] - 1)/k, {k, 1, nmax}]], {x, 0, nmax}], x] Range[0, nmax]!
a[n_] := a[n] = If[n == 0, 1, Sum[Sum[(-1)^(k/d + 1)/(d - 1)!, {d, Divisors[k]}] a[n - k], {k, 1, n}]/n]; Table[n! a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jun 18 2018
STATUS
approved