OFFSET
0,2
COMMENTS
The n-th term of the n-th binomial transform of A000108.
LINKS
N. J. A. Sloane, Transforms
FORMULA
a(n) = [x^n] (sqrt(1 - n*x) - sqrt(1 - 4*x - n*x))/(2*x*sqrt(1 - n*x)).
a(n) = A271025(n,n).
a(n) ~ exp(2) * (BesselI(0,2) - BesselI(1,2)) * n^n. - Vaclav Kotesovec, Sep 20 2017
a(n) = Sum_{k=0..n} binomial(n,k) * A000108(k) * n^(n-k). - Vaclav Kotesovec, Nov 23 2021
MATHEMATICA
Table[n!*SeriesCoefficient[E^((n+2)*x)*(BesselI[0, 2*x] - BesselI[1, 2*x]), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Sep 20 2017 *)
Join[{1}, Table[Sum[Binomial[n, j] * CatalanNumber[j] * n^(n-j), {j, 0, n}], {n, 1, 20}]] (* Vaclav Kotesovec, Nov 23 2021 *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Sep 20 2017
STATUS
approved