A047831 a(n) = Product_{i=1..n} ((i+5)*(i+6)*(i+7)*(i+8)*(i+9))/(i*(i+1)*(i+2)*(i+3)*(i+4)).

1, 252, 19404, 731808, 16818516, 267227532, 3184461423, 30107635272, 235234907908, 1566039386912, 9095857138368, 46960429261824, 218772384397632, 931020034054176, 3656383418054268, 13365232267026024, 45800747571406905, 148055097314224100

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• changed

Comments

Number of tilings of a <5,n,5> hexagon.

References

• O. D. Anderson, Find the next sequence, J. Rec. Math., 8 (No. 4, 1975-1976), 241.

Links

• Seiichi Manyama, Table of n, a(n) for n = 0..10000
• O. D. Anderson, Find the next sequence, J. Rec. Math., 8 (No. 4, 1975-1976), 241. [Annotated scanned copy]
• Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 25.

Crossrefs

Fifth row of array A103905.

Cf. A002117, A013663.

Programs

Maple

seq(binomial(n+5,n+4)*binomial(n+6,n+3)*binomial(n+7,n+2)*binomial(n+8,n+1)*binomial(n+9,n)/(140*5!), n=0..17); # Zerinvary Lajos, May 29 2007

Mathematica

Table[Product[Times@@(i+Range[5,9])/Times@@(i+Range[0,4]),{i,n}],{n,0,20}] (* Harvey P. Dale, Jan 30 2015 *)

PARI

a(n) = prod(k=1, 5, binomial(n+k+4, n-k+5))/(140*5!); \\ Seiichi Manyama, Apr 02 2021

Formula

a(n) = C(n+5,n+4)*C(n+6,n+3)*C(n+7,n+2)*C(n+8,n+1)*C(n+9,n)/(140*5!). - Zerinvary Lajos, May 29 2007

Sum_{n>=0} 1/a(n) = 876090600000*zeta(3) + 266716800000*zeta(5) - 5318707224821/4. - Amiram Eldar, Aug 31 2025

Extensions

Definition corrected by Daniel Soll (soll(AT)mathematik.uni-marburg.de), Aug 31 2004