A082145 A subdiagonal of number array A082137.

1, 5, 42, 336, 2640, 20592, 160160, 1244672, 9674496, 75246080, 585761792, 4564377600, 35602145280, 277970595840, 2172375244800, 16992801914880, 133035751833600, 1042374243778560, 8173537721057280, 64136851016908800, 503613708419727360, 3956964851869286400

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 )*binomial(2*n+3, n).

(n+3)*a(n) +2*(-7*n-13)*a(n-1) +24*(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) = 37/7 - 208*arcsin(1/(2*sqrt(2)))/(7*sqrt(7)).

Sum_{n>=0} (-1)^n/a(n) = 296*log(2)/27 - 61/9. (End)

Example

a(0) = ( 2^(-1)+(0^0)/2 )*C(3,0) = ( 1/2+1/2 )*1 = 1 (use 0^0 = 1). - clarified by Jon Perry, Oct 29 2014

Maple

Z:=(1-3*z-sqrt(1-4*z))/sqrt(1-4*z)/64: Zser:=series(Z, z=0, 32): seq(coeff(Zser*2^(n+1), z, n), n=4..23); # Zerinvary Lajos, Jan 01 2007

Mathematica

Join[{1}, Table[2^(n-1)* Binomial[2*n+3, n], {n, 1, 30}]] (* G. C. Greubel, Feb 05 2018 *)

Prog

(Magma) [(2^(n-1)+(0^n)/2)*Binomial(2*n+3, n): n in [0..30]]; // Vincenzo Librandi, Oct 30 2014
(PARI) for(n=0, 30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+3, n), ", ")) \\ G. C. Greubel, Feb 05 2018

Crossrefs

Cf. A069723, A082143, A082144.

Sequence in context: A062021 A241780 A215785 * A126765 A228793 A330628

Adjacent sequences: A082142 A082143 A082144 * A082146 A082147 A082148

Keyword

nonn,easy

Author

Paul Barry, Apr 06 2003

Status

approved