OFFSET
0,2
COMMENTS
The inverse binomial transform of a(n) is A002492(n) = 2n(n+1)(2n+1)/3.
FORMULA
Conjecture: a(n) = (2^(n-1)*n*(5+6*n+n^2))/3. G.f.: -4*x*(x-1) / (2*x-1)^4. - Colin Barker, Apr 06 2014
a(n) = (-1)^n * Sum_{k=0..floor(n/2)} binomial(n-k, k) * (-4)^(n-k) * (n-k). - Joseph M. Shunia, Jul 20 2022
MATHEMATICA
Table[Sum[2 Binomial[n, k] k (k + 1) (2 k + 1)/3, {k, 0, n}], {n, 0, 30}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Wesley Ivan Hurt, Apr 04 2014
STATUS
approved