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
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.
- Feihu Liu, Guoce Xin, and Chen Zhang, Ehrhart Polynomials of Order Polytopes: Interpreting Combinatorial Sequences on the OEIS, arXiv:2412.18744 [math.CO], 2024. See p. 13.
- Index entries for linear recurrences with constant coefficients, signature (12,-66,220,-495,792,-924,792,-495, 220,-66,12,-1).
Crossrefs
Programs
-
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
-
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 *) LinearRecurrence[{12,-66,220,-495,792,-924,792,-495,220,-66,12,-1},{1,37,478,3614,19490,82994,296438,923702,2580071,6588075,15606084,34685508},30] (* Harvey P. Dale, Dec 22 2024 *) -
PARI
for(n=1,30, print1(sum(i=1,n, binomial(i+4,5)^2), ", ")) \\ G. C. Greubel, Nov 22 2017
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)
Extensions
More terms from R. J. Mathar, Jun 16 2010