A014309 a(n) = (n+2)*(n+1)*(n^2 + 7*n - 12)/24.

-1, 3, 15, 40, 84, 154, 258, 405, 605, 869, 1209, 1638, 2170, 2820, 3604, 4539, 5643, 6935, 8435, 10164, 12144, 14398, 16950, 19825, 23049, 26649, 30653, 35090, 39990, 45384, 51304, 57783, 64855, 72555

Offset: 1

Author

N. J. A. Sloane

Keywords

• sign
• easy

Links

• Vincenzo Librandi, Table of n, a(n) for n = 1..725
• Index entries for linear recurrences with constant coefficients, signature (5,-10,10,-5,1).

Programs

GAP

List([1..40], n-> (n+2)*(n+1)*(n^2+7*n-12)/24); # G. C. Greubel, Jun 12 2019

Magma

[(n+2)*(n+1)*(n^2+7*n-12)/24: n in [1..40]]; // Vincenzo Librandi, Apr 25 2011

Mathematica

Table[(n+2)(n+1)(n^2+7n-12)/24,{n,40}]  (* Harvey P. Dale, Feb 20 2011 *)

PARI

{a(n) = (n+2)*(n+1)*(n^2+7*n-12)/24}; \\ G. C. Greubel, Jun 12 2019

Sage

[(n+2)*(n+1)*(n^2+7*n-12)/24 for n in (1..40)] # G. C. Greubel, Jun 12 2019

Formula

G.f.: x*(1 + x^4 - 5*x^3 + 10*x^2 - 8*x)/(x-1)^5. - Maksym Voznyy (voznyy(AT)mail.ru), Aug 10 2009

E.g.f.: (24 - (24 - 48*x^2 - 16*x^3 - x^4)*exp(x))/24. - G. C. Greubel, Jun 12 2019

a(n) = binomial(n+2,4) + 2*binomial(n+2,3) - binomial(n+2,2). - Étienne Tétreault, Sep 02 2020