cp's OEIS Frontend

This is a front-end for the Online Encyclopedia of Integer Sequences, made by Christian Perfect. The idea is to provide OEIS entries in non-ancient HTML, and then to think about how they're presented visually. The source code is on GitHub.

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.

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%I A132303 #9 Aug 30 2025 10:26:43
%S A132303 1,3,45,831,17181,375903,8530929,198643455,4714491357,113550338127,
%T A132303 2767105469745,68077260387315,1688160321677025,42142679453321307,
%U A132303 1058050429855640217,26695057057648257231,676431705046728704733,17205315843416998571415,439098128408223839364561,11239967518370464873317291
%N 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.
%H A132303 Robert Israel, <a href="/A132303/b132303.txt">Table of n, a(n) for n = 0..698</a>
%p A132303 f:= proc(n) local t; add(subs(x=1,t)^3, t = expand((1+x+x^2)^n)) end proc:
%p A132303 map(f, [$0..20]); # _Robert Israel_, Aug 29 2025
%o A132303 (PARI) a(n)=sum(k=0,2*n,polcoeff((1+x+x^2)^n,k)^3)
%Y A132303 Cf. A132304, A132305.
%K A132303 nonn,changed
%O A132303 0,2
%A A132303 _Paul D. Hanna_, Aug 18 2007