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A080929 Sequence associated with a(n) = 2*a(n-1) + k*(k+2)*a(n-2). 11
1, 3, 12, 40, 120, 336, 896, 2304, 5760, 14080, 33792, 79872, 186368, 430080, 983040, 2228224, 5013504, 11206656, 24903680, 55050240, 121110528, 265289728, 578813952, 1258291200, 2726297600, 5888802816, 12683575296, 27246198784 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

The third column of number triangle A080928.

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (6,-12,8)

FORMULA

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

For n>0, a(n) = (n+1)*(n+2)*2^(n-2). - Ralf Stephan, Jan 16 2004

a(n) = Sum_{k=0..n} Sum_{i=0..n} (k+1)*binomial(n-1,i). - Wesley Ivan Hurt, Sep 20 2017

MAPLE

[seq (ceil(binomial(n+2, 2)*2^(n-1)), n=0..27)]; # Zerinvary Lajos, Nov 01 2006

MATHEMATICA

CoefficientList[Series[(1 - x) (1 - 2 x + 4 x^2)/(1 - 2 x)^3, {x, 0, 27}], x] (* Michael De Vlieger, Sep 21 2017 *)

PROG

(MAGMA) [n eq 0 select 1 else (n+1)*(n+2)*2^(n-2): n in [0..40]]; // Vincenzo Librandi, Sep 22 2011

CROSSREFS

Essentially the same as A052482.

Cf. A082140, A082141, A082138, A082139, A080951, A080929, A057711.

Sequence in context: A032093 A007993 A293366 * A052482 A061136 A308648

Adjacent sequences:  A080926 A080927 A080928 * A080930 A080931 A080932

KEYWORD

nonn,easy

AUTHOR

Paul Barry, Feb 26 2003

STATUS

approved

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Last modified June 24 14:15 EDT 2019. Contains 324325 sequences. (Running on oeis4.)