OFFSET
0,3
FORMULA
a(0) = 0; a(n) = (-2)^(n-1) - (1/n) * Sum_{k=1..n-1} binomial(n,k)^2 * (-2)^k * (n-k) * a(n-k).
a(n) = 2^(n-1) * A002190(n).
MATHEMATICA
nmax = 17; CoefficientList[Series[-Log[BesselJ[0, 2 Sqrt[2 x]]]/2, {x, 0, nmax}], x] Range[0, nmax]!^2
a[0] = 0; a[n_] := a[n] = (-2)^(n - 1) - (1/n) Sum[Binomial[n, k]^2 (-2)^k (n - k) a[n - k], {k, 1, n - 1}]; Table[a[n], {n, 0, 17}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 04 2024
STATUS
approved