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URL: https://oeis.org/A135854

⇱ A135854 - OEIS

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A135854
a(n) = (n+1)*(2^n+1) for n > 0 with a(0)=1.
3
1, 6, 15, 36, 85, 198, 455, 1032, 2313, 5130, 11275, 24588, 53261, 114702, 245775, 524304, 1114129, 2359314, 4980755, 10485780, 22020117, 46137366, 96469015, 201326616, 419430425, 872415258, 1811939355, 3758096412
OFFSET
0,2
FORMULA
Binomial transform of [1, 5, 4, 8, 8, 12, 12, 16, 16, 20, 20, ...].
G.f.: 1 - x*(-6 + 21*x - 24*x^2 + 8*x^3) / ( (2*x-1)^2*(x-1)^2 ). - R. J. Mathar, Apr 04 2012
G.f.: (1 - 8*x^2 + 12*x^3 - 4*x^4)/((1-x)^2*(1-2*x)^2). - L. Edson Jeffery, Jan 14 2014
a(0) = 1, a(n) = (n+1)*(2^n+1), n>0. - L. Edson Jeffery, Jan 14 2014
E.g.f.: exp(x)*(1 + x + exp(x)*(1 + 2*x)) - 1. - Stefano Spezia, Dec 13 2021
EXAMPLE
a(3) = 15 = sum of row 3 terms of triangle A135853: (6 + 6 + 3).
a(4) = 36 = (1, 3, 3, 1) dot (1, 5, 4, 8) = (1 + 15 + 12 + 8).
MAPLE
A135854:=n->(n+1)*(2^n+1): 1, seq(A135854(n), n=1..50); # Wesley Ivan Hurt, Dec 07 2016
MATHEMATICA
Join[{1}, LinearRecurrence[{6, -13, 12, -4}, {6, 15, 36, 85}, 25]] (* G. C. Greubel, Dec 07 2016 *)
PROG
(PARI) Vec((1-8*x^2+12*x^3-4*x^4)/((1-x)^2*(1-2*x)^2) + O(x^50)) \\ G. C. Greubel, Dec 07 2016
CROSSREFS
Cf. A215149.
Row sums of triangle A135853.
Sequence in context: A177206 A128443 A245470 * A221905 A083011 A299267
KEYWORD
nonn,easy
AUTHOR
Gary W. Adamson, Dec 01 2007
EXTENSIONS
Corrected by R. J. Mathar, Apr 04 2012
STATUS
approved