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A056126 a(n) = n*(n + 17)/2. 21
0, 9, 19, 30, 42, 55, 69, 84, 100, 117, 135, 154, 174, 195, 217, 240, 264, 289, 315, 342, 370, 399, 429, 460, 492, 525, 559, 594, 630, 667, 705, 744, 784, 825, 867, 910, 954, 999, 1045, 1092, 1140, 1189, 1239, 1290, 1342, 1395, 1449, 1504, 1560, 1617, 1675 (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

G.f.: x*(9-8*x)/(1-x)^3.

a(n) = 3*a(n-1) - 3*a(n-2) + a(n-3).

a(n) = A126890(n,8) for n>7. - Reinhard Zumkeller, Dec 30 2006

If we define f(n,i,a) = Sum_{k=0..n-i} binomial(n,k)*stirling1(n-k,i)* Product_{j=0..k-1} (-a-j), then a(n) = -f(n,n-1,9), for n>=1. - Milan Janjic, Dec 20 2008

a(n) = a(n-1) + n + 8 (with a(0)=0). - Vincenzo Librandi, Aug 07 2010

a(n) = 9*n - floor(n/2) + floor(n^2/2). - Wesley Ivan Hurt, Jun 15 2013

E.g.f.: x*(18 + x)*exp(x)/2. - G. C. Greubel, Jan 19 2020

From Amiram Eldar, Jan 10 2021: (Start)

Sum_{n>=1} 1/a(n) = 2*A001008(17)/(17*A002805(17)) = 42142223/104144040.

Sum_{n>=1} (-1)^(n+1)/a(n) = 4*log(2)/17 - 1768477/20828808. (End)

MAPLE

seq( n*(n+17)/2, n=0..50); # G. C. Greubel, Jan 19 2020

MATHEMATICA

Table[n(n+17)/2, {n, 0, 50}] (* Harvey P. Dale, Apr 25 2011 *)

PROG

(PARI) a(n)=n*(n+17)/2 \\ Charles R Greathouse IV, Sep 24 2015

(MAGMA) [n*(n+17)/2: n in [0..50]]; // G. C. Greubel, Jan 19 2020

(Sage) [n*(n+17)/2 for n in (0..50)] # G. C. Greubel, Jan 19 2020

(GAP) List([0..50], n-> n*(n+17)/2 ); # G. C. Greubel, Jan 19 2020

CROSSREFS

Cf. A000096, A001477, A051942, A056000, A056121.

Cf. A001008, A002805, A098849, A120071, A132760, A132761, A132765.

Sequence in context: A017377 A330171 A189798 * A190513 A190576 A250663

Adjacent sequences:  A056123 A056124 A056125 * A056127 A056128 A056129

KEYWORD

easy,nonn

AUTHOR

Barry E. Williams, Jul 07 2000

STATUS

approved

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Last modified September 24 02:30 EDT 2021. Contains 347618 sequences. (Running on oeis4.)