A081890 a(n) = 9^n - 8^n - 7^n - 6^n + 3*5^n.

1, 3, 7, 33, 643, 11073, 151867, 1816713, 19996963, 208630833, 2099398027, 20597485593, 198424412083, 1885822419393, 17740469253787, 165580566245673, 1535948935336003, 14178113530908753, 130361707324735147, 1194785495130736953, 10921581632007328723, 99616564791408530913

Offset: 0

Author

Paul Barry, Mar 30 2003

Keywords

• easy
• nonn

Comments

Binomial transform of A081687.

Links

• Index entries for linear recurrences with constant coefficients, signature (35,-485,3325,-11274,15120).

Crossrefs

Cf. A081687, A081691.

Programs

Mathematica

LinearRecurrence[{35,-485,3325,-11274,15120},{1,3,7,33,643},30] (* Harvey P. Dale, Jun 26 2017 *)

Formula

G.f.: -(4182*x^4-2082*x^3+387*x^2-32*x+1)/((5*x-1)*(6*x-1)*(7*x-1)*(8*x-1)*(9*x-1)). [Colin Barker, Aug 12 2012]

From Elmo R. Oliveira, Sep 12 2024: (Start)

E.g.f.: exp(5*x)*(exp(4*x) - exp(3*x) - exp(2*x) - exp(x) + 3).

a(n) = 35*a(n-1) - 485*a(n-2) + 3325*a(n-3) - 11274*a(n-4) + 15120*a(n-5) for n > 4. (End)

Extensions

a(19)-a(21) from Elmo R. Oliveira, Sep 12 2024