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A027379 Expansion of (1+x^2-x^3)/(1-x)^3. 8
1, 3, 7, 12, 18, 25, 33, 42, 52, 63, 75, 88, 102, 117, 133, 150, 168, 187, 207, 228, 250, 273, 297, 322, 348, 375, 403, 432, 462, 493, 525, 558, 592, 627, 663, 700, 738, 777, 817, 858, 900, 943, 987, 1032, 1078 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (3,-3,1).

FORMULA

a(n) = n*(n+5)/2 = A000217(n+2)-3 for n>=1. - Emeric Deutsch, Mar 01 2004

a(n) = n + a(n-1) + 2, n>1. - Vincenzo Librandi, Dec 06 2009

E.g.f.: 1 + x*(x + 6)*exp(x)/2. - G. C. Greubel, May 14 2017

MATHEMATICA

f[1]=1; f[n_] := Sum[ Binomial[k+1, k ], {k, 2, n}]; Table[ f[n], {n, 1, 45}] # Zerinvary Lajos, Mar 31 2007

PROG

(PARI) a(n)=if(n, n*(n+5)/2, 1) \\ Charles R Greathouse IV, Jun 11 2015

CROSSREFS

Essentially the triangular numbers (A000217) minus 3. Also essentially the same as A055998. Cf. A034856, A046691.

Sequence in context: A140778 A095115 A141214 * A055998 A066379 A024517

Adjacent sequences:  A027376 A027377 A027378 * A027380 A027381 A027382

KEYWORD

nonn,easy

AUTHOR

N. J. A. Sloane

STATUS

approved

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Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)