A081584 Fourth row of Pascal-(1,2,1) array A081577.

1, 13, 79, 307, 886, 2086, 4258, 7834, 13327, 21331, 32521, 47653, 67564, 93172, 125476, 165556, 214573, 273769, 344467, 428071, 526066, 640018, 771574, 922462, 1094491, 1289551, 1509613, 1756729, 2033032, 2340736, 2682136, 3059608

Offset

0,2

Comments

Equals binomial transform of [1, 12, 54, 108, 81, 0, 0, 0, ...] where (1, 12, 54, 108, 81) = row 4 of triangle A013610. - Gary W. Adamson, Jul 19 2008

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Formula

a(n) = (8 + 6*n + 81*n^2 - 18*n^3 + 27*n^4)/8.

G.f.: (1+2*x)^4/(1-x)^5.

E.g.f.: (1/8)*(8 + 96*x + 216*x^2 + 144*x^3 + 27*x^4)*exp(x). - G. C. Greubel, May 26 2021

Maple

seq((8+6*n+81*n^2-18*n^3+27*n^4)/8, n=0..40); # G. C. Greubel, May 26 2021

Mathematica

CoefficientList[Series[(1+2x)^4/(1-x)^5, {x, 0, 40}], x] (* Vincenzo Librandi, Aug 09 2013 *)
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 13, 79, 307, 886}, 40] (* Harvey P. Dale, Sep 18 2024 *)

Prog

(Magma) [(8+6*n+81*n^2-18*n^3+27*n^4)/8: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013
(Sage) [(8+6*n+81*n^2-18*n^3+27*n^4)/8 for n in (0..40)] # G. C. Greubel, May 26 2021

Crossrefs

Cf. A013610, A081583.

Sequence in context: A041318 A142056 A173831 * A125323 A075584 A126481

Adjacent sequences: A081581 A081582 A081583 * A081585 A081586 A081587

Keyword

easy,nonn

Author

Paul Barry, Mar 23 2003

Status

approved