A086027 a(n) = Sum_{i=1..n} binomial(i+5,6)^2.

1, 50, 834, 7890, 51990, 265434, 1119210, 4063866, 13081875, 38131900, 102259964, 255425340, 600047436, 1336192860, 2838530460, 5783112156, 11350211925, 21540508734, 39656591950, 71021001950, 124026854850, 211648774950, 353581802550, 579225802950, 931794553575

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

Cf. A087127, A024166, A085438, A085439, A085440, A085441, A085442, A086020, A086021, A086022, A086023, A086024, A086025, A086026, A086028, A086029, A086030.

Sequence in context: A206120 A160287 A104672 * A110929 A329713 A101929

Adjacent sequences: A086024 A086025 A086026 * A086028 A086029 A086030

Keyword

easy,nonn

Author

André F. Labossière, Jul 11 2003

Extensions

More terms from R. J. Mathar, Jun 16 2010

Status

approved