A132303 Sum of cubes of trinomial coefficients: a(n) = Sum_{k=0..2n} trinomial(n,k)^3 where trinomial(n,k) = [x^k] (1 + x + x^2)^n.
1, 3, 45, 831, 17181, 375903, 8530929, 198643455, 4714491357, 113550338127, 2767105469745, 68077260387315, 1688160321677025, 42142679453321307, 1058050429855640217, 26695057057648257231, 676431705046728704733, 17205315843416998571415, 439098128408223839364561, 11239967518370464873317291
Offset: 0
Links
- Robert Israel, Table of n, a(n) for n = 0..698
Programs
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Maple
f:= proc(n) local t; add(subs(x=1,t)^3, t = expand((1+x+x^2)^n)) end proc: map(f, [$0..20]); # Robert Israel, Aug 29 2025
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PARI
a(n)=sum(k=0,2*n,polcoeff((1+x+x^2)^n,k)^3)