A171002 Binomial(n-k,k) * binomial(n-k-1,k+1) where k = ceiling(n/4).
0, 0, 0, 3, 0, 6, 40, 150, 100, 525, 1960, 5880, 7056, 26460, 83160, 228690, 365904, 1189188, 3435432, 9018009, 17177160, 51531480, 141581440, 361032672, 773641440, 2204878104, 5859116640, 14647791600, 34178180400, 93989996100, 243891989880, 601019546490
Offset: 1