A077539 a(n) = floor(T(n+1)!*T(n-1)!/(T(n)!)^2), where T(n) = n(n+1)/2 = the n-th triangular number.

6, 20, 42, 71, 108, 152, 204, 263, 330, 403, 485, 573, 669, 773, 884, 1002, 1128, 1261, 1401, 1549, 1704, 1866, 2036, 2214, 2398, 2591, 2790, 2997, 3211, 3433, 3662, 3898, 4142, 4394, 4652, 4918, 5192, 5472, 5761, 6056, 6359, 6669, 6987

Offset

1,1

Comments

The ratio itself is an integer only for n = 1, 2 and 3.

Links

Table of n, a(n) for n=1..43.

Example

a(1) = 6 = (2*3)/1;
a(2) = 20 = (4*5*6)/(2*3), etc.

Mathematica

Floor[(#[[1]]!*#[[3]]!)/(#[[2]]!)^2]&/@Partition[Accumulate[ Range[ 0, 50]], 3, 1] (* Harvey P. Dale, Aug 21 2015 *)

Crossrefs

Sequence in context: A369348 A143711 A338120 * A068377 A002943 A009946

Adjacent sequences: A077536 A077537 A077538 * A077540 A077541 A077542

Keyword

nonn

Author

Amarnath Murthy, Nov 09 2002

Extensions

More terms from Mark Hudson (mrmarkhudson(AT)hotmail.com), Feb 11 2003

Definition clarified by Harvey P. Dale, Aug 21 2015

Status

approved