A387515 a(n) = Sum_{k=0..floor(n/2)} 2^(n-2*k) * binomial(k,n-2*k)^2.
1, 0, 1, 2, 1, 8, 5, 18, 37, 40, 145, 178, 417, 872, 1301, 3330, 5365, 11080, 22801, 39362, 86721, 157128, 312293, 631666, 1169541, 2416104, 4602961, 9061458, 18123553, 34717608, 69825013, 135902818, 267384405, 531611656, 1035512785, 2060791650, 4048647489, 7979180296
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..2000
Programs
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Magma
[(&+[2^(n-2*k) * Binomial(k,n-2*k)^2: k in [0..Floor(n/2)]]): n in [0..40]]; // Vincenzo Librandi, Sep 01 2025
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Mathematica
Table[Sum[2^(n-2*k)*Binomial[k,n-2*k]^2,{k,0,Floor[n/2]}],{n,0,40}] (* Vincenzo Librandi, Sep 01 2025 *) -
PARI
a(n) = sum(k=0, n\2, 2^(n-2*k)*binomial(k, n-2*k)^2);
Formula
G.f.: 1/sqrt((1-x^2-2*x^3)^2 - 8*x^5).