A128057 -id:A128057 - cp's OEIS frontend

A128056 Hankel transform of A128057.

1, -3, -6, 28, 56, -288, -576, 3008, 6016, -31488, -62976, 329728, 659456, -3452928, -6905856, 36159488, 72318976, -378667008, -757334016, 3965452288, 7930904576, -41526755328, -83053510656, 434873827328

Offset: 0

Paul Barry, Feb 13 2007

a(n)=2^A128054(n)*A128053(n). Hankel transform of A128058.

a(n)=A128055(n)*((cos(pi*n/2)-sin(pi*n/2))((F(n-1)+F(n+1))(5/6-cos(pi*n/3)/3)(1+(-1)^n)/2 +(F(n)+F(n+2))(5/6-cos(pi*(n+1)/3)/3)(1-(-1)^n)/2)).

Empirical g.f.: -(2*x-1)*(4*x^2-x+1) / (16*x^4+12*x^2+1). - Colin Barker, Jun 27 2013

A128058 Expansion of 1/((1-x)sqrt(1-2x+5x^2)).

Original entry on oeis.org

1, 2, 1, -4, -9, 2, 43, 72, -53, -418, -549, 860, 4161, 4006, -11619, -41104, -24989, 145046, 399571, 89796, -1723259, -3787914, 829841, 19739016, 34642741, -26909998, -219300587, -300591148, 467328447, 2369124842

Offset: 0

Paul Barry, Feb 13 2007

Partial sums of A098331. Binomial transform of A128057. Hankel transform is A128056.

CoefficientList[Series[1/((1-x)Sqrt[1-2x+5x^2]),{x,0,50}],x] (* Harvey P. Dale, Jun 23 2018 *)

a(n)=sum{k=0..n, sum{j=0..k, C(k,j)*C(k-j,j)*(-1)^j}}

D-finite with recurrence: n*a(n) +(-3*n+1)*a(n-1) +(7*n-6)*a(n-2) +5*(-n+1)*a(n-3)=0. - R. J. Mathar, Jan 23 2020

cp's OEIS Frontend

A128056 Hankel transform of A128057.

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