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A081583
Third row of Pascal-(1,2,1) array A081577.
4
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
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
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 *)
LinearRecurrence[{4, -6, 4, -1}, {1, 10, 46, 136}, 60] (* Harvey P. Dale, Oct 01 2021 *)
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
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Mar 23 2003
STATUS
approved