OFFSET
1,2
LINKS
T. D. Noe, Table of n, a(n) for n = 1..1000
John Engbers and Christopher Stocker, Two Combinatorial Proofs of Identities Involving Sums of Powers of Binomial Coefficients, Integers 16 (2016), #A58.
Index entries for linear recurrences with constant coefficients, signature (14, -91, 364, -1001, 2002, -3003, 3432, -3003, 2002, -1001, 364, -91, 14, -1).
FORMULA
From R. J. Mathar, Jun 16 2010: (Start)
G.f.: x*(1 + 36*x + 225*x^2 + 400*x^3 + 225*x^4 + 36*x^5 + x^6)/(1-x)^14.
a(n) = n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(77*n^6 + 1386*n^5 + 9380*n^4 + 29400*n^3 + 41783*n^2 + 20874*n + 60)/518918400. (End)
MAPLE
A086027:=n->sum(binomial(i+5, 6)^2, i=1..n); seq(A086027(k), k=1..50); # Wesley Ivan Hurt, Oct 24 2013
MATHEMATICA
Table[Sum[Binomial[k + 5, 6]^2, {k, 1, n}], {n, 50}] (* Wesley Ivan Hurt, Oct 24 2013 *)
PROG
(PARI) vector(30, n, sum(i=1, n, binomial(i+5, 6)^2) ) \\ G. C. Greubel, Nov 22 2017
(Magma) [n*(n+1)*(n+2)*(n+3)*(n+4)*(n+5)*(n+6)*(77*n^6 +1386*n^5 +9380*n^4 + 29400*n^3 +41783*n^2 +20874*n +60)/518918400: n in [1..30]]; // G. C. Greubel, Nov 22 2017
(Sage) [sum(binomial(j+5, 6)^2 for j in (1..n)) for n in (1..30)] # G. C. Greubel, Aug 27 2019
(GAP) List([1..30], n-> Sum([1..n], j-> Binomial(j+5, 6)^2)); # G. C. Greubel, Aug 27 2019
CROSSREFS
KEYWORD
easy,nonn
AUTHOR
André F. Labossière, Jul 11 2003
EXTENSIONS
More terms from R. J. Mathar, Jun 16 2010
STATUS
approved