A264152 -id:A264152 - cp's OEIS frontend

A264153 a(n) = ((2*n)!)^2 / 2^n.

1, 2, 144, 64800, 101606400, 411505920000, 3585039575040000, 59375425441812480000, 1710012252724199424000000, 80059353648041568632832000000, 5780285333388601255290470400000000, 616883611349898303167109582028800000000, 93983451956379706284115479041251737600000000

Offset: 0

Peter Luschny, Nov 06 2015

nonn

Cf. A000079, A000680, A134372, A264152.

a := n -> (2*n)!^2/2^n; seq(a(n), n=0..10);

a = lambda n: factorial(2*n)^2 >> n
[a(n) for n in range(11)]

a(n) = A134372(n)/A000079(n).
a(n)*A264152(n) = A134372(n)*A006882(2*n-1)/A006882(n).
a(n)/A264152(n) is an integer: 1, 1, 24, 1620,....

A358361 Decimal expansion of the constant Sum_{j>=0} j!!/(2*j)!, where j!! indicates the double factorial of j.

Original entry on oeis.org

1, 5, 8, 7, 7, 0, 2, 6, 4, 7, 7, 2, 7, 6, 6, 0, 5, 0, 7, 9, 7, 1, 8, 0, 1, 2, 6, 6, 2, 8, 5, 5, 5, 3, 7, 3, 2, 2, 3, 5, 4, 8, 6, 2, 3, 2, 4, 6, 7, 7, 2, 1, 2, 5, 2, 7, 5, 1, 6, 3, 2, 0, 4, 7, 3, 5, 6, 6, 5, 1, 0, 4, 0, 4, 6, 7, 1, 8, 6, 9, 5, 4, 9, 5, 5, 2, 2

Offset: 1

Marco Ripà, Nov 12 2022

Sum_{j>=0} j!!/(2j)! converges since Sum_{j>=0} j!!/j! converges by A143280 (and it is trivial to note that (2*j)! >= j! for any positive integer j).

			1.587702647727...

Eric Weisstein's World of Mathematics, Double Factorial.

Cf. A006882, A010050, A143280, A264152.

RealDigits[1 + Sum[(i)!!/(2i)!, {i,1,200}], 10, 105][[1]]

Equals Sum_{j>=0} A006882(j)/A010050(j).

Equals Sum_{j>=0} 1/(A264152(j)*j!).

cp's OEIS Frontend

A264153 a(n) = ((2*n)!)^2 / 2^n.

Views

Author

Keywords

Crossrefs

Programs

Maple

Sage

Formula

A358361 Decimal expansion of the constant Sum_{j>=0} j!!/(2*j)!, where j!! indicates the double factorial of j.

Views

Author

Keywords

Comments

Examples

Links

Crossrefs

Programs

Mathematica

Formula