A124133 a(n)=(-1/2)*sum_{i1+i2+i3=2n} ((2*n)!/(i1! i2! i3!))*B(i1) where B are the Bernoulli numbers.

0, 5, 28, 123, 506, 2041, 8184, 32759, 131062, 524277, 2097140, 8388595, 33554418, 134217713, 536870896, 2147483631, 8589934574, 34359738349, 137438953452, 549755813867, 2199023255530, 8796093022185, 35184372088808