A111602 Third column (m=2) of unsigned triangle A111595.

1, 6, 42, 300, 2475, 22050, 220500, 2381400, 28279125, 360186750, 4970577150, 73045872900, 1150472498175, 19174541636250, 339663308985000, 6333077180430000, 124682456989715625, 2572020969902133750

Offset: 2

Author

Wolfdieter Lang, Aug 23 2005

Keywords

• nonn
• easy

Formula

E.g.f.: (1/sqrt(1-x^2))*((x/(1-x))^2)/2!.

a(n) = (n!/2!)*Sum_{k=0..floor((n-2)/2)} binomial(2*k, k)*(n-2*k-1)/(4^k), n >= 2.

D-finite with recurrence (-n+2)*a(n) +2*n*a(n-1) +n*(n-1)^2*a(n-2)=0. - R. J. Mathar, Aug 11 2025