A052144 a(n) = A000172(n)^2.

1, 4, 100, 3136, 119716, 5071504, 230553856, 11016601600, 546360462244, 27888242788624, 1456587070867600, 77515424509446400, 4189899499315360000, 229472379264509977600, 12709952101698593689600, 710863065714510068187136

Offset: 0

Author

N. J. A. Sloane, Jan 23 2000

Keywords

• nonn
• easy

References

• R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see page 191.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..500

Crossrefs

Cf. A000172.

Programs

Mathematica

A052144[n_] := HypergeometricPFQ[{-n, -n, -n}, {1, 1}, -1]^2;
Array[A052144, 20, 0] (* Paolo Xausa, Jan 30 2024, after Jean-François Alcover in A000172 *)

Formula

P-recursive: P(n-1)*n^4*a(n) = P(n)*Q(n)*a(n-1) + 8*P(n-1)*Q(n)*a(n-2) - 512*P(n)*(n-2)^4*a(n-3), where P(n) = 7*n^2 - 7*n + 2 and Q(n) = 57*n^4 - 228*n^3 + 321*n^2 - 186*n + 40 with a(0) = 1, a(1) = 4 and a(2) = 100. - Peter Bala, Feb 01 2024

a(n) ~ 2^(6*n+2) / (3*Pi^2*n^2). - Vaclav Kotesovec, Feb 02 2024