A383755 -id:A383755 - cp's OEIS frontend

A383756 Expansion of 1/Product_{k=0..2} (1 - 3^k * 4^(2-k) * x).

1, 37, 925, 19525, 375661, 6828757, 119609725, 2042733925, 34274529421, 567869330677, 9323118394525, 152047784616325, 2467581667044781, 39901653896747797, 643493505828795325, 10356906506162786725, 166444482073618177741, 2671936126059753592117

Offset: 0

Seiichi Manyama, May 09 2025

Index entries for linear recurrences with constant coefficients, signature (37,-444,1728).

Cf. A383755.

a(n) = (3*9^(n+1)-7*12^(n+1)+4*16^(n+1))/7;

def a(n): return 3^(2*n)*q_binomial(n+2, 2, 4/3)

a(n) = A383755(n+2,2).
a(n) = 3^(2*n) * q-binomial(n+2, 2, 4/3).
G.f.: exp( Sum_{k>=1} f(3*k)/f(k) * x^k/k ), where f(k) = 4^k - 3^k.
a(n) = (3*9^(n+1) - 7*12^(n+1) + 4*16^(n+1))/7.
a(n) = 37*a(n-1) - 444*a(n-2) + 1728*a(n-3).

A383757 Expansion of 1/Product_{k=0..3} (1 - 3^k * 4^(3-k) * x).

Original entry on oeis.org

1, 175, 19525, 1776775, 144142141, 10884484975, 783802527925, 54630820881175, 3721247723926381, 249337226367003775, 16508103305566548325, 1083453420457687217575, 70652392978007927384221, 4585369275138131990546575, 296541443098920894741800725, 19127262646595562017053105975

Offset: 0

Seiichi Manyama, May 09 2025

Index entries for linear recurrences with constant coefficients, signature (175,-11100,302400,-2985984).

Cf. A383755.

a(n) = (-27^(n+2)+111*36^(n+1)-148*48^(n+1)+64^(n+2))/259;

def a(n): return 3^(3*n)*q_binomial(n+3, 3, 4/3)

a(n) = A383755(n+3,3).
a(n) = 3^(3*n) * q-binomial(n+3, 3, 4/3).
G.f.: exp( Sum_{k>=1} f(4*k)/f(k) * x^k/k ), where f(k) = 4^k - 3^k.
a(n) = (-27^(n+2) + 111*36^(n+1) - 148*48^(n+1) + 64^(n+2))/259.
a(n) = 175*a(n-1) - 11100*a(n-2) + 302400*a(n-3) - 2985984*a(n-4).

cp's OEIS Frontend

A383756 Expansion of 1/Product_{k=0..2} (1 - 3^k * 4^(2-k) * x).

Views

Author

Keywords

Links

Crossrefs

Programs

PARI

Sage

Formula