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A081583 Third row of Pascal-(1,2,1) array A081577. 3
1, 10, 46, 136, 307, 586, 1000, 1576, 2341, 3322, 4546, 6040, 7831, 9946, 12412, 15256, 18505, 22186, 26326, 30952, 36091, 41770, 48016, 54856, 62317, 70426, 79210, 88696, 98911, 109882, 121636, 134200, 147601, 161866, 177022, 193096 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Equals binomial transform of [1, 9, 27, 27, 0, 0, 0,...] where (1, 9, 27, 27) = row 3 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 (4,-6,4,-1).

FORMULA

a(n) = (2 + 9*n + 9*n^3)/2.

G.f.: (1+2*x)^3/(1-x)^4.

a(n) = hypergeommetric2F1([-n, -3], [1], 3). - Peter Luschny, Nov 19 2014

E.g.f.: (1/2)*(2 + 18*x + 27*x^2 + 9*x^3)*exp(x). - G. C. Greubel, May 25 2021

MAPLE

seq((2+9*n+9*n^3)/2, n=0..40); # G. C. Greubel, May 25 2021

MATHEMATICA

CoefficientList[Series[(1+2x)^3/(1-x)^4, {x, 0, 50}], x] (* Vincenzo Librandi, Aug 09 2013 *)

PROG

(MAGMA) [(2+9*n+9*n^3)/2: n in [0..40]]; // Vincenzo Librandi, Aug 09 2013

(Sage)

a = lambda n: hypergeometric([-n, -3], [1], 3)

[simplify(a(n)) for n in range(36)] # Peter Luschny, Nov 19 2014

CROSSREFS

Cf. A013610, A038764, A081584, A081577.

Sequence in context: A248575 A341404 A320697 * A244246 A288117 A213834

Adjacent sequences:  A081580 A081581 A081582 * A081584 A081585 A081586

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Mar 23 2003

STATUS

approved

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Last modified August 5 01:51 EDT 2021. Contains 346456 sequences. (Running on oeis4.)