OFFSET
0,5
FORMULA
E.g.f.: log(1 + Sum_{k>=1} Pell(k)*x^k/k!).
a(0) = 0; a(n) = Pell(n) - (1/n)*Sum_{k=1..n-1} binomial(n,k)*Pell(n-k)*k*a(k).
MAPLE
seq(n!*coeff(series(log(1+exp(x)*sinh(sqrt(2)*x)/sqrt(2)), x=0, 26), x, n), n=0..25); # Paolo P. Lava, Jan 29 2019
MATHEMATICA
FullSimplify[nmax = 25; CoefficientList[Series[Log[1 + Exp[x] Sinh[Sqrt[2] x]/Sqrt[2]], {x, 0, nmax}], x] Range[0, nmax]!]
a[n_] := a[n] = Fibonacci[n, 2] - Sum[Binomial[n, k] Fibonacci[n - k, 2] k a[k], {k, 1, n - 1}]/n; a[0] = 0; Table[a[n], {n, 0, 25}]
CROSSREFS
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Jan 25 2019
STATUS
approved