A082144 A subdiagonal of number array A082137.

1, 4, 30, 224, 1680, 12672, 96096, 732160, 5601024, 42997760, 331082752, 2556051456, 19778969600, 153363087360, 1191302553600, 9268801044480, 72219408138240, 563445537177600, 4401135695953920, 34414895667609600, 269374774271016960, 2110381254330286080

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

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

(n+2)*a(n) +12*(-n-1)*a(n-1) +16*(2*n-1)*a(n-2)=0. - R. J. Mathar, Oct 29 2014

From Amiram Eldar, Jan 16 2024: (Start)

Sum_{n>=0} 1/a(n) = 88*arccot(sqrt(7))/(7*sqrt(7)) - 3/7.

Sum_{n>=0} (-1)^n/a(n) = 52*log(2)/27 - 5/9. (End)

Example

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

Mathematica

Join[{1}, Table[2^(n-1)*Binomial[2*n+2, n], {n, 1, 50}]] (* G. C. Greubel, Feb 05 2018 *)

Prog

(PARI) for(n=0, 30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+2, n), ", ")) \\ G. C. Greubel, Feb 05 2018
(Magma) [(2^(n-1) + 0^n/2)*Binomial(2*n+2, n): n in [0..30]]; // G. C. Greubel, Feb 05 2018

Crossrefs

Cf. A069723, A082137, A082143, A082145.

Sequence in context: A007905 A084976 A000313 * A349456 A220727 A137971

Adjacent sequences: A082141 A082142 A082143 * A082145 A082146 A082147

Keyword

easy,nonn

Author

Paul Barry, Apr 06 2003

Status

approved