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

Author

Paul Barry, Feb 04 2009

Keywords

• easy
• nonn

Comments

Hankel transform of A007272 is 10,35,84,... with g.f. (10-5x+4x^2-x^3)/(1-x)^4.

Hankel transform of A156125 is 10^(n^2-1+0^n)*A156126(n).

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

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

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