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.

1, 3, 309, 32847, 4775301, 764206503, 131689759209, 23857704965727, 4487745064421061, 869024373004460823, 172218243516497425809, 34778752398142969125627, 7134304921516864247956281, 1482965360342923597534988883, 311760492785929879483633778049

Offset: 0

Author

Paul D. Hanna, Aug 18 2007

Keywords

• nonn
• changed

Comments

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

Crossrefs

Cf. A027907, A082758, A132303, A132304.

Programs

PARI

a(n)=sum(k=0,2*n,polcoeff((1+x+x^2)^n,k)^5)