A132304 Sum of fourth powers of trinomial coefficients: a(n) = Sum_{k=0..2n} trinomial(n,k)^4 where trinomial(n,k) = [x^k] (1 + x + x^2)^n.

1, 3, 115, 5157, 281907, 16688953, 1043460469, 67769148555, 4527813298227, 309207348577017, 21487099512128265, 1514508365575327455, 108015601963868232885, 7780760215720406500095, 565264860408377433558523, 41369186303433709127364757, 3047140179357736909766753331

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, A132305.

Programs

PARI

a(n)=sum(k=0,2*n,polcoeff((1+x+x^2)^n,k)^4)