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A008978 (5n)!/(n!)^5. 7
1, 120, 113400, 168168000, 305540235000, 623360743125120, 1370874167589326400, 3177459078523411968000, 7656714453153197981835000, 19010638202652030712978200000, 48334775757901219912115629238400 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Number of paths of length 5n in Z^5 from (0,0,0,0,0) to (n,n,n,n,n).

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..100

V. Batyrev, Review of "Mirror Symmetry and Algebraic Geometry", by D. A. Cox and S. Katz, Bull. Amer. Math. Soc., 37 (No. 4, 2000), 473-476.

R. M. Dickau, 5-D shortest path diagrams

FORMULA

a(n) ~ 5^(5*n+1/2) / (4 * Pi^2 * n^2). - Vaclav Kotesovec, Mar 07 2014

MATHEMATICA

Table[(5 n)!/(n)!^5, {n, 0, 20}] (* Vincenzo Librandi, Mar 08 2014 *)

PROG

(MAGMA) [Factorial(5*n)/Factorial(n)^5: n in [0..10]]; // Vincenzo Librandi, Mar 08 2014

(PARI) a(n) = (5*n)!/(n!)^5; \\ Michel Marcus, Mar 08 2014

CROSSREFS

Cf. A000984, A006480, A008977.

Sequence in context: A184887 A159735 A157879 * A077692 A184127 A068296

Adjacent sequences:  A008975 A008976 A008977 * A008979 A008980 A008981

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified December 21 20:27 EST 2014. Contains 252326 sequences.