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 (5,-10,10,-5,1).
FORMULA
a(n) = N(5, n) = Sum_{k>0} A001263(5, k)*n^(k-1) = n^4 +10*n^3 +20*n^2 +10*n +1.
G.f.: (1 +37*x -3*x^2 -13*x^3 +2*x^4)/(1-x)^5. - Philippe Deléham, Apr 03 2013
E.g.f.: (1 +41*x +57*x^2 +16*x^3 +x^4)*exp(x). - G. C. Greubel, Feb 16 2021
MAPLE
MATHEMATICA
LinearRecurrence[{5, -10, 10, -5, 1}, {1, 42, 197, 562, 1257}, 40] (* Harvey P. Dale, Mar 06 2020 *)
PROG
(PARI) a(n) = n^4+10*n^3+20*n^2+10*n+1 \\ Charles R Greathouse IV, Jan 17 2012
(Sage) [n^4 +10*n^3 +20*n^2 +10*n +1 for n in (0..40)] # G. C. Greubel, Feb 16 2021
(Magma) [n^4 +10*n^3 +20*n^2 +10*n +1: n in [0..40]]; // G. C. Greubel, Feb 16 2021
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Philippe Deléham, Jan 22 2004
EXTENSIONS
Corrected by T. D. Noe, Nov 08 2006
STATUS
approved