A027814 a(n) = 126*(n+1)*binomial(n+5,9)/5.
126, 1512, 9702, 44352, 162162, 504504, 1387386, 3459456, 7963956, 17153136, 34918884, 67721472, 125919612, 225629712, 391270572, 658982016, 1081142370, 1732250520, 2716483770, 4177293120, 6309453150, 9374044680, 13716915030, 19791233280, 28184836680
Offset: 4
Links
- T. D. Noe, Table of n, a(n) for n = 4..1000
- Index entries for linear recurrences with constant coefficients, signature (11,-55,165,-330,462,-462,330,-165,55,-11,1).
Crossrefs
Cf. A062264.
Programs
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Magma
A027814:= func< n | 126*(n+1)*Binomial(n+5,9)/5 >; [A027814(n): n in [4..50]]; // G. C. Greubel, Mar 05 2025
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Mathematica
Table[126(n+1)Binomial[n+5,9]/5,{n,4,40}] (* Harvey P. Dale, Mar 13 2011 *) -
SageMath
def A027814(n): return 126*(n+1)*binomial(n+5,9)//5 print([A027814(n) for n in range(4,41)]) # G. C. Greubel, Mar 05 2025
Formula
G.f.: 126*(1+x)*x^4/(1-x)^11.
a(n) = C(n+1, 5)*C(n+5, 5). - Zerinvary Lajos, Apr 18 2005; corrected by R. J. Mathar, Feb 10 2016
From Amiram Eldar, Feb 03 2022: (Start)
Sum_{n>=4} 1/a(n) = 25*Pi^2/6 - 1160419/28224.
Sum_{n>=4} (-1)^n/a(n) = 25*Pi^2/12 - 27625/1344. (End)
Comments