OFFSET
2,2
COMMENTS
a(n) is the coefficient of x^n/n! in the Taylor series expansion of B(A(x)) where A(x)= Sum_{positive integers relatively prime to n}x^n/n and B(x)=x^2/2!.
LINKS
Andrew Howroyd, Table of n, a(n) for n = 2..200
FORMULA
a(p) = A000254(p-1) for prime p.
MATHEMATICA
f[list_]:=x^First[list]/First[list]+x^Last[list]/Last[list];
Prepend[Table[a=Total[Map[f, Select[IntegerPartitions[n, 2], Apply[GCD, #]==1&]]]; Last[Range[0, n]! CoefficientList[Series[a^2/2!, {x, 0, n}], x]], {n, 3, 30}], 1]
PROG
(PARI) a(n)={sum(k=1, n-1, if(gcd(k, n-k)==1, binomial(n, k)*(k-1)!*(n-k-1)!))/2} \\ Andrew Howroyd, Mar 27 2020
CROSSREFS
KEYWORD
nonn
AUTHOR
Geoffrey Critzer, Oct 12 2011
EXTENSIONS
Terms a(19) and beyond from Andrew Howroyd, Mar 27 2020
STATUS
approved