A292700 1/4 of the number of paths that are made of alternate vertical and horizontal 4*n consecutive prime (> 2 and < prime(4*n+2)) steps. (Each path begins and ends at the same point but is allowed to intersect itself.)

0, 0, 0, 2, 4, 40, 756, 8466, 70664, 788240, 11086299, 114208465, 1536869680, 19129734630, 228346732944, 3059857239120, 38601632542723, 509554928113867, 6793745301391293, 92409631618813044, 1240139159309482820, 16995549322569645324, 236256012348427662180

Offset: 1

Author

Seiichi Manyama, Sep 21 2017

Keywords

• nonn

Examples

			U, D, L and R express up, down, left and right.
n = 4:
3R, 5U, 7L, 11D, 13L, 17U, 19R, 23U, 29L, 31U, 37R, 41U, 43R, 47D, 53L, 59D.
3R, 5U, 7L, 11U, 13L, 17D, 19R, 23U, 29L, 31U, 37R, 41D, 43R, 47U, 53L, 59D.
		

Crossrefs

Cf. A000040, A007219, A292698, A292699.

Formula

Constant term in the expansion of (1/4) * Product_{k=1..2*n} (x^prime(2*k) + 1/x^prime(2*k)) * Product_{k=1..2*n} (y^prime(2*k+1) + 1/y^prime(2*k+1)).

a(n) = A292698(n) * A292699(n).