OFFSET
1,4
LINKS
Alois P. Heinz, Table of n, a(n) for n = 1..426
FORMULA
E.g.f. A(x) satisfies differential equation A''(x)=log(1/(1-A(x)), A'(0)=1, A''(0)=1. - Vladimir Kruchinin, Nov 18 2011
a(n) = n!*b(n), b(n) = b(n-2)*(n-2) + sum(i=0..n-4, b(i+3)*(i+1)*(i+2)*(i+3)*b(n-3-i)))/(n*(n-1)*(n-2)) n > 0, b(1)=1, b(2)=1/2. - Vladimir Kruchinin, Nov 18 2011
MATHEMATICA
CIJ[p_] := -Log[1 - p];
seq[n_] := Module[{p}, p = x + O[x]^(Mod[n, 2] + 1); Do[p = Integrate[1 + Integrate[1 + CIJ[p], x], x], {i, 1, n/2}]; CoefficientList[p/x, x]* Range[n]!];
seq[23] (* Jean-François Alcover, Oct 06 2019, after Andrew Howroyd *)
PROG
(Maxima)
a(n):=if n<3 then 1/n! else (a(n-2)*(n-2)+sum(a(i+3)*(i+1)*(i+2)*(i+3)*a(n-3-i), i, 0, n-4))/(n*(n-1)*(n-2));
makelist(n!*a(n), n, 1, 17); /* Vladimir Kruchinin, Nov 18 2011 */
(PARI)
CIJ(p)={-log(1-p)}
seq(n)={my(p=x+O(x*x^(n%2))); for(i=1, n\2, p=intformal(1 + intformal(1 + CIJ(p)))); Vec(serlaplace(p))} \\ Andrew Howroyd, Sep 19 2018
CROSSREFS
KEYWORD
nonn,eigen
AUTHOR
STATUS
approved