A132686 - OEIS

%I #9 Mar 14 2021 20:40:01

%S 1,5,36,455,12650,962598,237093780,209004408899,689960224294614,

%T 8639439963148103450,409865407260324119340236,

%U 73328394245057556170201283726,49287010273876375495535472789937580

%N a(n) = binomial(2^n + 2*n + 1, n).

%H G. C. Greubel, <a href="/A132686/b132686.txt">Table of n, a(n) for n = 0..50</a>

%F a(n) = [x^n] 1/(1-x)^(2^n + n + 2).

%t Table[Binomial[2^n +2*n +1, n], {n,0,20}] (* _G. C. Greubel_, Mar 13 2021 *)

%o (PARI) a(n)=binomial(2^n+2*n+1,n)

%o (Sage) [binomial(2^n +2*n +1, n) for n in (0..20)] # _G. C. Greubel_, Mar 13 2021

%o (Magma) [Binomial(2^n +2*n +1, n): n in [0..20]]; // _G. C. Greubel_, Mar 13 2021

%Y Sequences of the form binomial(2^n +p*n +q, n): A136556 (0,-1), A014070 (0,0), A136505 (0,1), A136506 (0,2), A060690 (1,-1), A132683 (1,0), A132684 (1,1), A132685 (2,0), this sequence (2,1), A132687 (3,-1), A132688 (3,0), A132689 (3,1).

%Y Cf. A136555.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 26 2007