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.
%I A132305 #10 Aug 31 2025 10:32:31
%S A132305 1,3,309,32847,4775301,764206503,131689759209,23857704965727,
%T A132305 4487745064421061,869024373004460823,172218243516497425809,
%U A132305 34778752398142969125627,7134304921516864247956281,1482965360342923597534988883,311760492785929879483633778049
%N A132305 Sum of fifth powers of trinomial coefficients: a(n) = Sum_{k=0..2n} trinomial(n,k)^5 where trinomial(n,k) = [x^k] (1 + x + x^2)^n.
%C A132305 Conjecture: the supercongruence a(n*p^k) == a(n*p^(k-1)) (mod p^(2*k)) holds for all primes p >= 5 and positive integers n and k. - _Peter Bala_, Aug 29 2025
%o A132305 (PARI) a(n)=sum(k=0,2*n,polcoeff((1+x+x^2)^n,k)^5)
%Y A132305 Cf. A027907, A082758, A132303, A132304.
%K A132305 nonn,changed
%O A132305 0,2
%A A132305 _Paul D. Hanna_, Aug 18 2007