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

Author

Paul Barry, Mar 23 2003

Keywords

• easy
• nonn

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).

Crossrefs

Cf. A013610, A081583.

Programs

Magma

[(8+6*n+81*n^2-18*n^3+27*n^4)/8: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013

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 *)

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

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