OFFSET
0,3
COMMENTS
Inverse binomial transform of A001003.
FORMULA
a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n,k)*A001003(k).
a(n) ~ 2^(n - 1/4) * (1 + sqrt(2))^(n - 1/2) / (sqrt(Pi) * n^(3/2)). - Vaclav Kotesovec, Feb 23 2019
D-finite with recurrence: (n+1)*a(n) +3*(-n+1)*a(n-1) +2*(-4*n+5)*a(n-2) +4*(-n+2)*a(n-3)=0. - R. J. Mathar, Jan 25 2020
MATHEMATICA
nmax = 27; CoefficientList[Series[2/(1 + 2 x + Sqrt[1 - 4 x (1 + x)]), {x, 0, nmax}], x]
Table[Sum[(-1)^(n - k) Binomial[n, k] Hypergeometric2F1[1 - k, -k, 2, 2], {k, 0, n}], {n, 0, 27}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Feb 21 2019
STATUS
approved