A156126 Sequence related to Hankel transform of super-ballot numbers.
1, 35, 84, 165, 286, 455, 680, 969, 1330, 1771, 2300, 2925, 3654, 4495, 5456, 6545, 7770, 9139, 10660, 12341, 14190, 16215, 18424, 20825, 23426, 26235, 29260, 32509, 35990, 39711, 43680
Offset: 0
Links
- Vincenzo Librandi, Table of n, a(n) for n = 0..1000
- Index entries for linear recurrences with constant coefficients, signature (4,-6,4,-1).
Programs
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Magma
I:=[1, 35, 84, 165, 286]; [n le 5 select I[n] else 4*Self(n-1)-6*Self(n-2)+4*Self(n-3)-Self(n-4): n in [1..50]]; // Vincenzo Librandi, Jun 30 2012
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Mathematica
CoefficientList[Series[(1+31x-50x^2+35x^3-9x^4)/(1-x)^4,{x,0,40}],x] (* Vincenzo Librandi, Jun 30 2012 *) LinearRecurrence[{4,-6,4,-1},{1,35,84,165,286},40] (* Harvey P. Dale, Mar 25 2022 *)
Formula
G.f.: (1+31x-50x^2+35x^3-9x^4)/(1-x)^4.
a(n) = (2*n+5)*(2*n+3)*(n+2)/3, n>0. - R. J. Mathar, Oct 13 2011
Comments