A027379 Expansion of (1+x^2-x^3)/(1-x)^3.

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

Offset: 0

Author

N. J. A. Sloane

Keywords

• nonn
• easy

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).

Crossrefs

Essentially the triangular numbers (A000217) minus 3.

Also essentially the same as A055998.

Cf. A000217, A034856, A046691.

Programs

Magma

[n eq 0 select 1 else n*(n+5)/2: n in [0..50]]; // G. C. Greubel, Jul 31 2022

PARI

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

SageMath

[n*(n+5)/2 + bool(n==0) for n in (0..50)] # G. C. Greubel, Jul 31 2022

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