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A081584 Fourth row of Pascal-(1,2,1) array A081577. 3
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 (list; graph; refs; listen; history; text; internal format)
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 *)

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

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Last modified August 1 14:14 EDT 2021. Contains 346391 sequences. (Running on oeis4.)