A296770 - OEIS

%I #6 Dec 24 2017 10:22:09

%S 1,5,24,111,500,2210,9632,41531,177564,754014,3184016,13382710,

%T 56026984,233765636,972504704,4035441491,16707488684,69033916166,

%U 284733161264,1172510645666,4821324991064,19799091571676,81208982686784,332726301861086,1361862906980120

%N Row sums of A050158.

%F a(n) = Sum_{k=0..n} (binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1)).

%F a(n) = 4^n*((2*(n + 2)*Gamma(n + 3/2))/(sqrt(Pi)*Gamma(n + 2)) - 1).

%F a(n) = (n/2+1)*binomial(2*(n+1), n+1) - 4^n.

%F a(n) ~ 4^n*(2*sqrt(n/Pi) - 1).

%F a(n) = A002457(n) - A008549(n).

%p A296770 := n -> add(binomial(2*n+1, n+1) - binomial(2*n+1, n-k-1), k=0..n):

%p seq(A296770(n), n=0..24);

%t a[n_] := 4^n ((2 (2 + n) Gamma[3/2 + n])/(Sqrt[Pi] Gamma[2 + n]) - 1);

%t Table[a[n], {n, 0, 24}]

%Y Cf. A002457, A008549, A050158.

%K nonn

%O 0,2

%A _Peter Luschny_, Dec 22 2017