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
Examples
a(0)=(2^(-1)+(0^0)/2)C(2,0)=2*(1/2)=1 (use 0^0=1).
Links
- G. C. Greubel, Table of n, a(n) for n = 0..1000
Programs
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Magma
[(2^(n-1) + 0^n/2)*Binomial(2*n+2,n): n in [0..30]]; // G. C. Greubel, Feb 05 2018
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Mathematica
Join[{1}, Table[2^(n-1)*Binomial[2*n+2, n], {n,1,50}]] (* G. C. Greubel, Feb 05 2018 *) -
PARI
for(n=0,30, print1((2^(n-1) + 0^n/2)*Binomial(2*n+2,n), ", ")) \\ G. C. Greubel, Feb 05 2018
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)