A387480 a(n) = Sum_{k=0..n} 3^k * 2^(n-k) * binomial(k,n-k)^2.
1, 3, 15, 99, 603, 3807, 24759, 162243, 1072683, 7147359, 47887767, 322330995, 2178055899, 14765637663, 100380161655, 684061007139, 4671543976587, 31962145170015, 219043736154711, 1503380943222867, 10332034575214779, 71092843087100319, 489712662842798007
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
Programs
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Magma
[&+[3^k * 2^(n-k) * Binomial(k, n-k)^2: k in [0..n]]: n in [0..25]]; // Vincenzo Librandi, Sep 01 2025
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Mathematica
Table[Sum[3^k*2^(n-k)*Binomial[k,n-k]^2,{k,0,n}],{n,0,25}] (* Vincenzo Librandi, Sep 01 2025 *) -
PARI
a(n) = sum(k=0, n, 3^k*2^(n-k)*binomial(k, n-k)^2);
Formula
G.f.: 1/sqrt((1-3*x-6*x^2)^2 - 72*x^3).