A387476 a(n) = Sum_{k=0..floor(n/2)} 2^k * binomial(k,n-2*k)^2.
1, 0, 2, 2, 4, 16, 12, 72, 88, 264, 608, 1056, 3280, 5504, 15328, 31904, 71104, 175488, 358080, 900736, 1925248, 4518016, 10404864, 23138304, 54970624, 122038272, 286077440, 651510272, 1492685824, 3465687040, 7876488192, 18322630656, 41904609280, 96788580352, 223335882752
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Programs
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Magma
[(&+[2^k * Binomial(k,n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // Vincenzo Librandi, Aug 31 2025
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Mathematica
Table[Sum[2^k* Binomial[k,n-2*k]^2,{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Aug 31 2025 *) -
PARI
a(n) = sum(k=0, n\2, 2^k*binomial(k, n-2*k)^2);
Formula
G.f.: 1/sqrt((1-2*x^2-2*x^3)^2 - 16*x^5).