A113956 Expansion of (1/((1-4x)c(x)))/(1-x^2c(x)/sqrt(1-4x)), c(x) the g.f. of A000108.

1, 3, 12, 48, 194, 787, 3199, 13017, 52997, 215831, 879076, 3580511, 14582842, 59388280, 241829963, 984609111, 4008282780, 16315179752, 66399357417, 270193396769, 1099323033137, 4472155924094, 18190769442979, 73982564102230

Offset

0,2

Comments

Diagonal sums of A113955.

Links

Table of n, a(n) for n=0..23.

Formula

G.f.: (1+sqrt(1-4x))/(sqrt(1-4x)(sqrt(1-4x)(x+2)-x)); a(n)=sum{k=0..floor(n/2), sum{j=0..n-k, C(j, j-k)C(2n-2k, n-k-j)}}.

Conjecture D-finite with recurrence: n*a(n) +2*(-5*n+4)*a(n-1) +(27*n-46)*a(n-2) +(5*n-2)*a(n-3) +(-57*n+188)*a(n-4) +2*(-21*n+83)*a(n-5) +4*(-2*n+9)*a(n-6)=0. - R. J. Mathar, Jan 24 2020

Mathematica

CoefficientList[Series[(1+Sqrt[1-4x])/(2-x(7+Sqrt[1-4x]+4x)), {x, 0, 30}], x] (* Harvey P. Dale, Feb 10 2015 *)

Crossrefs

Sequence in context: A077828 A002001 A164346 * A323261 A103943 A283679

Adjacent sequences: A113953 A113954 A113955 * A113957 A113958 A113959

Keyword

easy,nonn

Author

Paul Barry, Nov 09 2005

Status

approved