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A160765
Expansion of (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.
1
1, 18, 112, 403, 1071, 2356, 4558, 8037, 13213, 20566, 30636, 44023, 61387, 83448, 110986, 144841, 185913, 235162, 293608, 362331, 442471, 535228, 641862, 763693, 902101, 1058526, 1234468, 1431487, 1651203, 1895296, 2165506, 2463633, 2791537
OFFSET
0,2
COMMENTS
Source: the De Loera et al. article and the Haws website listed in A160747.
FORMULA
G.f.: (1+13*x+32*x^2+13*x^3+x^4)/(1-x)^5.
a(n) = (n^2+n+1)*(5*n^2+5*n+2)/2. - R. J. Mathar, Sep 11 2011
a(n) = A000566(A002061(n+1)). - Bruno Berselli, Jul 31 2015
E.g.f.: (1/2)*(5*x^4 + 40*x^3 + 77*x^2 + 34*x + 2)*exp(x). - G. C. Greubel, Apr 26 2018
MATHEMATICA
Table[(n^2 + n + 1) (5 n^2 + 5 n + 2)/2, {n, 0, 40}] (* Bruno Berselli, Jul 31 2015 *)
PROG
(Sage) [(n^2+n+1)*(5*n^2+5*n+2)/2 for n in (0..40)] # Bruno Berselli, Jul 31 2015
(Magma) [(n^2+n+1)*(5*n^2+5*n+2)/2: n in [0..40]] // Bruno Berselli, Jul 31 2015
(PARI) for(n=0, 30, print1((n^2+n+1)*(5*n^2+5*n+2)/2, ", ")) \\ G. C. Greubel, Apr 26 2018
CROSSREFS
Sequence in context: A289393 A213562 A041622 * A192511 A324623 A244866
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Nov 18 2009
STATUS
approved