A086025 a(n) = Sum_{i=1..n} C(i+4,5)^2.

1, 37, 478, 3614, 19490, 82994, 296438, 923702, 2580071, 6588075, 15606084, 34685508, 72976852, 146387476, 281597860, 521971876, 936053677, 1629533233, 2761788434, 4568378450, 7391175350, 11718183750, 18235516650, 27894475050, 41997225075, 62305185111

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 (12,-66,220,-495,792,-924,792,-495, 220,-66,12,-1).

Formula

From R. J. Mathar, Jun 16 2010: (Start)

G.f.: x*(1+x)*(x^4+24*x^3+76*x^2+24*x+1)/(x-1)^12.

a(n) = n*(2*n+5)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(63*n^4 +630*n^3 +1855*n^2 +1400*n +12) / 19958400. (End)

Mathematica

Table[n*(2*n+5)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(63*n^4 +630*n^3 +1855*n^2 +1400*n +12)/19958400, {n, 1, 30}] (* G. C. Greubel, Nov 22 2017 *)

Prog

(PARI) for(n=1, 30, print1(sum(i=1, n, binomial(i+4, 5)^2), ", ")) \\ G. C. Greubel, Nov 22 2017
(Magma) [n*(2*n+5)*(n+5)*(n+4)*(n+3)*(n+2)*(n+1)*(63*n^4 +630*n^3 +1855*n^2 +1400*n +12)/19958400: n in [1..30]]; // G. C. Greubel, Nov 22 2017

Crossrefs

Cf. A087127, A024166, A085438, A085439, A085440, A085441, A085442, A086020, A086021, A086022, A086023, A086024, A086026, A086027, A086028, A086029, A086030.

Sequence in context: A142286 A166132 A342901 * A197215 A264419 A197240

Adjacent sequences: A086022 A086023 A086024 * A086026 A086027 A086028

Keyword

easy,nonn

Author

André F. Labossière, Jul 11 2003

Extensions

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

Status

approved