OFFSET
0,2
COMMENTS
Central terms of the triangle in A132121.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..5000
Index entries for linear recurrences with constant coefficients, signature (5, -10, 10, -5, 1).
FORMULA
G.f.: x*(11 + 55*x + 29*x^2 + x^3)/(1-x)^5. - Emeric Deutsch, Aug 19 2007
a(n) = 5*a(n-1) - 10*a(n-2) + 10*a(n-3) - 5*a(n-4) + a(n-5); a(0)=0, a(1)=11, a(2)=110, a(3)=469, a(4)=1356. - Harvey P. Dale, Jun 02 2015
E.g.f.: x*(33 + 132*x + 86*x^2 + 12*x^3)*exp(x)/3. - G. C. Greubel, Mar 16 2019
MAPLE
seq((1/3)*n*(2*n+1)*(6*n^2+4*n+1), n=0..32); # Emeric Deutsch, Aug 19 2007
MATHEMATICA
Table[n(2n+1)(6n^2+4n+1)/3, {n, 0, 40}] (* or *) LinearRecurrence[{5, -10, 10, -5, 1}, {0, 11, 110, 469, 1356}, 40] (* Harvey P. Dale, Jun 02 2015 *)
PROG
(PARI) {a(n) = n*(2*n+1)*(6*n^2+4*n+1)/3}; \\ G. C. Greubel, Mar 16 2019
(Magma) [n*(2*n+1)*(6*n^2+4*n+1)/3: n in [0..40]]; // G. C. Greubel, Mar 16 2019
(Sage) [n*(2*n+1)*(6*n^2+4*n+1)/3 for n in (0..40)] # G. C. Greubel, Mar 16 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Reinhard Zumkeller, Aug 12 2007
STATUS
approved