A386918 a(n) = 2^n * binomial(4*n,n).
1, 8, 112, 1760, 29120, 496128, 8614144, 151557120, 2692684800, 48201359360, 868004380672, 15706806542336, 285362317180928, 5202031080243200, 95104728494899200, 1743063914667048960, 32016101348447354880, 589188508080622534656, 10861173739509105295360
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..350
Programs
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Magma
[2^n * Binomial(4*n,n): n in [0..26]]; // Vincenzo Librandi, Aug 11 2025
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Mathematica
Table[2^n*Binomial[4*n,n],{n,0,30}] (* Vincenzo Librandi, Aug 11 2025 *) -
PARI
a(n) = 2^n*binomial(4*n, n);
Formula
a(n) = Sum_{k=0..n} binomial(4*n,k) * binomial(4*n-k,n-k).
a(n) = [x^n] (1+x)^(4*n)/(1-x)^(3*n+1).
a(n) = [x^n] 1/(1-2*x)^(3*n+1).
a(n) = [x^n] (1+2*x)^(4*n).