

A073617


Consider Pascal's triangle A007318; a(n) = product of terms at +45 degrees slope with the horizontal.


5



1, 1, 1, 2, 3, 12, 30, 240, 1050, 16800, 132300, 4233600, 61122600, 3911846400, 104886381600, 13425456844800, 674943865596000, 172785629592576000, 16407885372638760000, 8400837310791045120000, 1515727634953623371280000
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OFFSET

0,4


COMMENTS

The sum of the terms pertaining to the above product is the nth Fibonacci number: 1 + 5 + 6 + 1 = 13.
n divides A073617(n+1) for n>=1; see the Mathematica section. [Clark Kimberling, Feb 29 2012]


LINKS

Table of n, a(n) for n=0..20.


FORMULA

A073617(n+1)=product[C(n+1k,k) : 1<=k<=floor((n+1)/2)] for n>=1.
a(2n+1)/a(2n1)= binomial(2n,n); a(2n)/a(2n2)=(1/2)*binomial(2n,n); (a(2n+1)*a(2n2))/(a(2n)*a(2n1))]=2  John Molokach, Sep 09 2013


EXAMPLE

The seventh diagonal is 1,5,6,1 and product of the terms = 30 hence a(6) = 30.


MATHEMATICA

p[n_] := Product[Binomial[n + 1  k, k], {k, 1, Floor[(n + 1)/2]}]
Table[p[n], {n, 1, 20}] (* A073617(n+1) *)
Table[p[n]/n, {n, 1, 20}] (* A208649 *)
( * Clark Kimberling, Feb 29 2012 *)


CROSSREFS

Cf. A073618, A007685, A208649, A000984.
Sequence in context: A105401 A325595 A256031 * A034381 A076424 A165301
Adjacent sequences: A073614 A073615 A073616 * A073618 A073619 A073620


KEYWORD

nonn


AUTHOR

Amarnath Murthy, Aug 07 2002


EXTENSIONS

More terms from Antonio G. Astudillo (afg_astudillo(AT)lycos.com), Mar 22 2003


STATUS

approved



