A387481 a(n) = Sum_{k=0..floor(n/2)} 3^k * 2^(n-2*k) * binomial(k,n-2*k)^2.
1, 0, 3, 6, 9, 72, 63, 486, 1053, 2808, 11907, 22518, 99225, 246888, 755487, 2554902, 6488829, 23112216, 63506835, 198653958, 623336553, 1781565192, 5807475711, 16898655942, 52699192029, 161995971384, 484990399395, 1525112887446, 4572778238649, 14184781485480, 43472894580063
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Programs
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Magma
[(&+[3^k * 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[3^k * 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, 3^k*2^(n-2*k)*binomial(k, n-2*k)^2);
Formula
G.f.: 1/sqrt((1-3*x^2-6*x^3)^2 - 72*x^5).