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
Links
- Index entries for linear recurrences with constant coefficients, signature (65,-1482,14040,-46656).
Programs
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PARI
a(n) = (-8^(n+2)+38*12^(n+1)-57*18^(n+1)+27^(n+2))/95;
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Sage
def a(n): return 2^(3*n)*q_binomial(n+3, 3, 3/2)
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).