OFFSET
0,5
REFERENCES
R. P. Stanley, Enumerative Combinatorics, Cambridge, Vol. 2, 1999; see Problem 5.5.
LINKS
G. C. Greubel, Table of n, a(n) for n = 0..1000
Chai Wah Wu, Graphs whose normalized Laplacian matrices are separable as density matrices in quantum mechanics, arXiv:1407.5663 [quant-ph], 2014.
Index entries for linear recurrences with constant coefficients, signature (7,-21,35,-35,21,-7,1).
FORMULA
a(n) = (n-3)*(n-2)*(n-1)*n*(n^2 + 3*n + 4)/48.
G.f.: x^4*(16-2*x+x^2)/(1-x)^7. - Colin Barker, May 08 2012
E.g.f.: x^4*(32 + 12*x + x^2)*exp(x)/48. - G. C. Greubel, May 15 2019
MATHEMATICA
Table[Binomial[n, 4]*(n^2+3*n+4)/2, {n, 0, 40}] (* G. C. Greubel, May 15 2019 *)
LinearRecurrence[{7, -21, 35, -35, 21, -7, 1}, {0, 0, 0, 0, 16, 110, 435}, 40] (* Harvey P. Dale, Nov 24 2022 *)
PROG
(PARI) {a(n) = binomial(n, 4)*(n^2+3*n+4)/2}; \\ G. C. Greubel, May 15 2019
(Magma) [Binomial(n, 4)*(n^2+3*n+4)/2: n in [0..40]]; // G. C. Greubel, May 15 2019
(Sage) [binomial(n, 4)*(n^2+3*n+4)/2 for n in (0..40)] # G. C. Greubel, May 15 2019
(GAP) List([0..40], n-> Binomial(n, 4)*(n^2+3*n+4)/2) # G. C. Greubel, May 15 2019
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
N. J. A. Sloane, Jan 16 2000
STATUS
approved