%I #11 Mar 14 2021 20:40:10

%S 1,4,36,560,17550,1370754,324540216,267212177232,822871715492970,

%T 9728874233306696390,442491588454024774291770,

%U 76919746769405407508866898400,50743487119356450255156023756871000

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

%H G. C. Greubel, <a href="/A132687/b132687.txt">Table of n, a(n) for n = 0..50</a>

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

%t Table[Binomial[2^n+3n-1,n],{n,0,20}] (* _Harvey P. Dale_, Sep 07 2017 *)

%o (PARI) a(n)=binomial(2^n+3*n-1,n)

%o (Sage) [binomial(2^n +3*n -1, n) for n in (0..20)] # _G. C. Greubel_, Mar 13 2021

%o (Magma) [Binomial(2^n +3*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), A132686 (2,1), this sequence (3,-1), A132688 (3,0), A132689 (3,1).

%Y Cf. A136555.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Aug 26 2007