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A082143 First subdiagonal of number array A082137. 6
1, 3, 20, 140, 1008, 7392, 54912, 411840, 3111680, 23648768, 180590592, 1384527872, 10650214400, 82158796800, 635361361920, 4924050554880, 38233804308480, 297374033510400, 2316387208396800, 18067820225495040 (list; graph; refs; listen; history; text; internal format)
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)

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 * A009156 A074573 A068571

Adjacent sequences:  A082140 A082141 A082142 * A082144 A082145 A082146

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Apr 06 2003

STATUS

approved

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Last modified February 17 17:59 EST 2020. Contains 331999 sequences. (Running on oeis4.)