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A156126
Sequence related to Hankel transform of super-ballot numbers.
2
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
0,2
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).
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
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 *)
PROG
(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
CROSSREFS
Sequence in context: A201632 A044173 A044554 * A119691 A220007 A115393
KEYWORD
easy,nonn
AUTHOR
Paul Barry, Feb 04 2009
STATUS
approved