A383719 a(n) = Pell(n) * Pell(n-1) * Pell(n-2) * Pell(n-3) * Pell(n-4) / 3480.

1, 70, 5915, 482664, 39618670, 3248730940, 266442347522, 21851425660680, 1792084691254935, 146972777186757522, 12053560080255418725, 988538895611708641200, 81072243052956528402380, 6648912468496274313591800, 545291894670184984544154100, 44720584275276797753993516592

Offset: 5

Author

Seiichi Manyama, May 07 2025

Keywords

• nonn
• easy

Links

• Index entries for linear recurrences with constant coefficients, signature (70,1015,-2436,-1015,70,1).

Crossrefs

Fifth column of triangle A099927.

Cf. A000129.

Programs

PARI

pell(n) = ([2, 1; 1, 0]^n)[2, 1];
p(n, k) = prod(j=0, k-1, pell(n-j));
a(n) = p(n, 5)/p(5, 5);

Sage

def a(n): return ((1+sqrt(2))^(5*(n-5))*q_binomial(n, 5, -(3-2*sqrt(2)))).simplify_full()

Formula

G.f.: x^5 * exp( Sum_{k>=1} Pell(6*k)/Pell(k) * x^k/k ).

G.f.: x^5 / ((1-2*x-x^2) * (1+14*x-x^2) * (1-82*x-x^2)).

a(n) = 70*a(n-1) + 1015*a(n-2) - 2436*a(n-3) - 1015*a(n-4) + 70*a(n-5) + a(n-6).

a(n) = (1 + sqrt(2))^(5*(n-5)) * q-binomial(n, 5, -(sqrt(2) - 1)^2).