A082143 First subdiagonal of number array A082137.

1, 3, 20, 140, 1008, 7392, 54912, 411840, 3111680, 23648768, 180590592, 1384527872, 10650214400, 82158796800, 635361361920, 4924050554880, 38233804308480, 297374033510400, 2316387208396800, 18067820225495040, 141101072237199360, 1103153837490831360

Offset

0,2

Links

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

Formula

a(n) = (2^(n-1) + 0^n/2)*C(2n+1, n).

Conjecture: (n+1)*a(n) +4*(-2*n-1)*a(n-1)=0. - R. J. Mathar, Oct 19 2014

From Reinhard Zumkeller, Jan 15 2015: (Start)

a(n) = A000079(n-1) * A001700(n), for n > 0.

a(n) = A069720(n+1)/2. (End)

From Amiram Eldar, Jan 16 2024: (Start)

Sum_{n>=0} 1/a(n) = 64*arcsin(1/(2*sqrt(2)))/(7*sqrt(7)) + 1/7.

Sum_{n>=0} (-1)^n/a(n) = 32*log(2)/27 - 1/9. (End)

Example

a(0)=(2^(-1)+(0^0)/2)C(1,0)=2*(1/2)=1 (use 0^0=1).

Mathematica

Join[{1}, Table[2^(n-1)* Binomial[2*n+1, n], {n, 1, 30}]] (* G. C. Greubel, Feb 05 2018 *)

Prog

(Haskell)
a082143 0 = 1
a082143 n = (a000079 $ n - 1) * (a001700 n)
-- Reinhard Zumkeller, Jan 15 2015
(PARI) for(n=0, 30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+1, n), ", ")) \\ G. C. Greubel, Feb 05 2018
(Magma) [(2^(n-1) + 0^n/2)*Binomial(2*n+1, n): n in [0..30]]; // G. C. Greubel, Feb 05 2018

Crossrefs

Cf. A069723, A082144, A082145.

Cf. A000079, A001700, A069720.

Sequence in context: A267899 A073514 A163065 * A342055 A371411 A009156

Adjacent sequences: A082140 A082141 A082142 * A082144 A082145 A082146

Keyword

easy,nonn

Author

Paul Barry, Apr 06 2003

Status

approved