A157125 -id:A157125 - cp's OEIS frontend

A157127 A transform of the Catalan numbers with a simple Hankel transform.

1, 0, -1, -1, 1, 2, 1, -3, -5, -1, 11, 15, -5, -44, -41, 51, 169, 85, -303, -611, -15, 1513, 2021, -1271, -6827, -5673, 10361, 28301, 10141, -61102, -107015, 20109, 310387, 356515, -354349, -1421913, -936805, 2567875, 5930631, 972819, -14696329

Offset: 0

Paul Barry, Feb 23 2009

Hankel transform is A157128. Partial sums of A157125.

G.f.: (sqrt(1+x^2+4x^3)-sqrt(1+x^2))/(2*sqrt(1+x^2));

a(n)=sum{k=0..n, A157125(k)};

A157126 Expansion of (1-2x-3x^2+x^3-x^5)/(1+4x^3+x^6).

Original entry on oeis.org

1, -2, -3, -3, 8, 11, 11, -30, -41, -41, 112, 153, 153, -418, -571, -571, 1560, 2131, 2131, -5822, -7953, -7953, 21728, 29681, 29681, -81090, -110771, -110771, 302632, 413403, 413403, -1129438, -1542841, -1542841, 4215120, 5757961, 5757961

Offset: 0

Paul Barry, Feb 23 2009

Hankel transform of A157125.

Index entries for linear recurrences with constant coefficients, signature (0,0,-4,0,0,-1).

Cf. A048788.

CoefficientList[Series[(1-2x-3x^2+x^3-x^5)/(1+4x^3+x^6),{x,0,40}],x] (* or *) LinearRecurrence[{0,0,-4,0,0,-1},{1,-2,-3,-3,8,11},40] (* Harvey P. Dale, Jan 16 2013 *)

a(0)=1, a(1)=-2, a(2)=-3, a(3)=-3, a(4)=8, a(5)=11, a(n)=-4*a(n-3)-a(n-6). - Harvey P. Dale, Jan 16 2013

cp's OEIS Frontend

A157127 A transform of the Catalan numbers with a simple Hankel transform.

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A157126 Expansion of (1-2x-3x^2+x^3-x^5)/(1+4x^3+x^6).

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