OFFSET
0,4
LINKS
Seiichi Manyama, Table of n, a(n) for n = 0..457
FORMULA
a(0) = 0; a(n) = binomial(n,2) - (1/n) * Sum_{k=1..n-1} binomial(n,k) * binomial(n-k,2) * k * a(k).
a(n) = n! * Sum_{k=1..floor(n/2)} (-1)^(k-1) * k^(n-2*k-1)/(2^k * (n-2*k)!). - Seiichi Manyama, Dec 14 2023
MATHEMATICA
nmax = 23; CoefficientList[Series[Log[1 + x^2 Exp[x]/2], {x, 0, nmax}], x] Range[0, nmax]!
a[0] = 0; a[n_] := a[n] = Binomial[n, 2] - (1/n) Sum[Binomial[n, k] Binomial[n - k, 2] k a[k], {k, 1, n - 1}]; Table[a[n], {n, 0, 23}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Aug 01 2021
STATUS
approved