A383754 Expansion of 1/Product_{k=0..3} (1 - 2^k * 3^(3-k) * x).

1, 65, 2743, 96005, 3041143, 90873965, 2619766591, 73828050725, 2050312110055, 56398823205725, 1541678963379919, 41967937119356885, 1139327805030810487, 30873653666483535245, 835604944706085813727, 22597672980558843070085, 610791835087816964370439

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Index entries for linear recurrences with constant coefficients, signature (65,-1482,14040,-46656).

Formula

a(n) = A383753(n+3,3).

a(n) = 2^(3*n) * q-binomial(n+3, 3, 3/2).

G.f.: exp( Sum_{k>=1} f(4*k)/f(k) * x^k/k ), where f(k) = 3^k - 2^k.

a(n) = (-8^(n+2) + 38*12^(n+1) - 57*18^(n+1) + 27^(n+2))/95.

a(n) = 65*a(n-1) - 1482*a(n-2) + 14040*a(n-3) - 46656*a(n-4).

Prog

(PARI) a(n) = (-8^(n+2)+38*12^(n+1)-57*18^(n+1)+27^(n+2))/95;
(SageMath)
def a(n): return 2^(3*n)*q_binomial(n+3, 3, 3/2)

Crossrefs

Cf. A006101, A383753.

Sequence in context: A016111 A217675 A237858 * A075474 A069225 A211960

Adjacent sequences: A383751 A383752 A383753 * A383755 A383756 A383757

Keyword

nonn,easy

Author

Seiichi Manyama, May 09 2025

Status

approved