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A082145 A subdiagonal of number array A082137. 5

%I

%S 1,5,42,336,2640,20592,160160,1244672,9674496,75246080,585761792,

%T 4564377600,35602145280,277970595840,2172375244800,16992801914880,

%U 133035751833600,1042374243778560,8173537721057280,64136851016908800

%N A subdiagonal of number array A082137.

%H G. C. Greubel, <a href="/A082145/b082145.txt">Table of n, a(n) for n = 0..1000</a>

%F a(n) = ( 2^(n-1) + (0^n)/2 )*binomial(2*n+3, n).

%F (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

%e 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

%p 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

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

%o (MAGMA) [(2^(n-1)+(0^n)/2)*Binomial(2*n+3, n): n in [0..30]]; // _Vincenzo Librandi_, Oct 30 2014

%o (PARI) for(n=0,30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+3,n), ", ")) \\ _G. C. Greubel_, Feb 05 2018

%Y Cf. A069723, A082143, A082144.

%K nonn,easy

%O 0,2

%A _Paul Barry_, Apr 06 2003

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Last modified November 12 22:16 EST 2019. Contains 329079 sequences. (Running on oeis4.)