A327021 a(n) = (2*n-1)! / 2^(n-1) if n > 0 and a(0) = 1.

1, 1, 3, 30, 630, 22680, 1247400, 97297200, 10216206000, 1389404016000, 237588086736000, 49893498214560000, 12623055048283680000, 3786916514485104000000, 1329207696584271504000000, 539658324813214230624000000, 250941121038144617240160000000, 132496911908140357902804480000000

Offset: 0

Author

Peter Luschny, Aug 20 2019

Keywords

• nonn

Comments

A shifted version of A007019.

Crossrefs

Cf. A007019.

Programs

Maple

A327021 := n -> `if`(n = 0, 1, (2*n-1)! / 2^(n-1)): seq(A327021(n), n = 0..17);
# Alternative:
a := proc(n) option remember; if n < 2 then return 1 fi;
((2*(n-2)^3 + (n-2)^2)*a(n-2) + (2*(n-2)^3 + 9*(n-2)^2 + 12*n-18)*a(n-1))/n end:

Formula

a(n) = ((2*(n-2)^3 + (n-2)^2)*a(n-2) + (2*(n-2)^3 + 9*(n-2)^2 + 12*n-18)*a(n-1))/n for n >= 2.