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A002999 Expansion of (1+x*exp(x))^2. 3
1, 2, 6, 18, 56, 170, 492, 1358, 3600, 9234, 23060, 56342, 135192, 319514, 745500, 1720350, 3932192, 8912930, 20054052, 44826662, 99614760, 220201002, 484442156, 1061158958, 2315255856, 5033164850, 10905190452, 23555211318, 50734301240, 108984795194 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

T. D. Noe, Table of n, a(n) for n = 0..500

Index entries for linear recurrences with constant coefficients, signature (8,-25,38,-28,8)

FORMULA

a(0) = 1, a(n) = (n^2-n)2^n/4 + 2n. a(n) = A003013(n) + n = A001815(n) + 2n. - Ralf Stephan, Sep 02 2003

G.f.: 1+(2x(7x^3-10x^2+5x-1))/((x-1)^2 (2x-1)^3) [From Harvey P. Dale, Apr 04 2011]

MATHEMATICA

CoefficientList[Series[1+(2x(7x^3-10x^2+5x-1))/((x-1)^2 (2x-1)^3), {x, 0, 30}], x]  (* Harvey P. Dale, Apr 04 2011 *)

Table[If[n == 0, 1, (n^2 - n) 2^n/4 + 2*n], {n, 0, 30}] (* T. D. Noe, Apr 04 2011 *)

CROSSREFS

Cf. A048482, A001787, A005183.

Sequence in context: A148457 A182881 A291730 * A291228 A091142 A275857

Adjacent sequences:  A002996 A002997 A002998 * A003000 A003001 A003002

KEYWORD

nonn

AUTHOR

N. J. A. Sloane.

STATUS

approved

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Last modified August 14 17:44 EDT 2018. Contains 313751 sequences. (Running on oeis4.)