OFFSET
0,2
LINKS
Horst Alzer and Helmut Prodinger, Identities and Inequalities for Sums Involving Binomial Coefficients, INTEGERS 20 (2020) A9.
FORMULA
a(n) = Sum_{k=0..n} binomial(n, k)*k*Sum_{j=0..k} binomial(n, j).
G.f.: x*(1/(1 - 4*x)^2 + 1/(1 - 4*x)^(3/2)). - Stefano Spezia, Nov 28 2020
MATHEMATICA
a[n_] := n*(2^(2*n - 2) + Binomial[2*n, n]/2); Array[a, 26, 0] (* Amiram Eldar, Nov 28 2020 *)
PROG
(PARI) a(n) = n*2^(2*n-2) + n*binomial(2*n, n)/2;
(PARI) a(n) = sum(k=0, n, binomial(n, k)*k*sum(j=0, k, binomial(n, j)));
CROSSREFS
KEYWORD
nonn
AUTHOR
Michel Marcus, Nov 28 2020
STATUS
approved