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A036827 a(n) = 26+2^(n+1)*(-13+9*n-3*n^2+n^3). 6
0, 2, 34, 250, 1274, 5274, 19098, 63002, 194074, 567322, 1591322, 4317210, 11395098, 29392922, 74350618, 184942618, 453378074, 1097334810, 2626158618, 6222250010, 14610858010, 34032582682, 78693531674, 180757725210, 412685959194 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

M. Petkovsek et al., A=B, Peters, 1996, p. 97.

LINKS

Reinhard Zumkeller, Table of n, a(n) for n = 0..1000

S. Sykora, Finite and Infinite Sums of the Power Series (k^p)(x^k), DOI 10.3247/SL1Math06.002, Section V.

Index entries for linear recurrences with constant coefficients, signature (9, -32, 56, -48, 16).

FORMULA

a(n) = Sum_{k=0..n} 2^k*k^3. - Benoit Cloitre, Jun 11 2003

G.f.: (-2*x*(4*x^2+8*x+1))/((x-1)*(2*x-1)^4). [Maksym Voznyy (voznyy(AT)mail.ru), Jul 26 2009]

a(n) = 9*a(n-1)-32*a(n-2)+56*a(n-3)-48*a(n-4)+16*a(n-5) for n>4 with a(0)=0, a(1)=2, a(2)=34, a(3)=250, a(4)=1274. - Harvey P. Dale, Dec 15 2011

a(n) = Sum_{k=0..n} Sum_{i=0..n} k^3 * C(k,i). - Wesley Ivan Hurt, Sep 21 2017

EXAMPLE

a(3) = 2^0*0^3 + 2^1*1^3 + 2^2*2^3 + 2^3*3^3 = 250.

MATHEMATICA

Table[26 + 2^(n+1) (-13 + 9n - 3n^2 + n^3), {n, 0, 30}] (* or *) LinearRecurrence[ {9, -32, 56, -48, 16}, {0, 2, 34, 250, 1274}, 31] (* Harvey P. Dale, Dec 15 2011 *)

PROG

(Haskell)

a036827 n = 2^(n+1) * (n^3 - 3*n^2 + 9*n - 13) + 26

-- Reinhard Zumkeller, May 24 2012

(PARI) a(n)=26+2^(n+1)*(-13+9*n-3*n^2+n^3) \\ Charles R Greathouse IV, Oct 07 2015

CROSSREFS

Cf. A232599, A232600, A232601, A232602.

Sequence in context: A206624 A131471 A318268 * A136362 A220507 A263689

Adjacent sequences:  A036824 A036825 A036826 * A036828 A036829 A036830

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified April 24 12:01 EDT 2019. Contains 322429 sequences. (Running on oeis4.)