A027991 a(n) = Sum{T(n,k)*T(n,2n-k)}, 0<=k<=n-1, T given by A027926.

1, 3, 12, 40, 130, 404, 1227, 3653, 10720, 31090, 89316, 254568, 720757, 2029095, 5684340, 15855964, 44061862, 122032508, 336966015, 927953705, 2549229256, 6987648358, 19115124552, 52194037200, 142274514025, 387215773899

Offset

1,2

Comments

From Wolfdieter Lang, Jan 02 2012: (Start)

a(n) = A024458(2*n-1), n>=1 (bisection, odd arguments).

chate(n):=a(n+1), n>=0, is the even part of the bisection of the half-convolution of the sequence A000045(n+1), n>=0, with itself. See a comment on A201204 for the definition of half-convolution. There one finds also the rule for the o.g.f.s of the bisection. Here the o.g.f. of the sequence chate(n), n>=0, is Chate(x):= (Ce(x)+U2(x))/2 with Ce(x)=(1-x+x^2)/(1-3*x+x^2)^2, the o.g.f. of A054444(n), and

U2(x)=(1-x)/((1+x)*(1-3*x+x^2)), the o.g.f. of A007598(n+1), n>=0. This results (after multiplying with x) in the o.g.f. given below in the formula section. It is equivalent to the explicit formula given there, as can be seen after a partial fraction decomposition of the o.g.f.

(End)

Links

Table of n, a(n) for n=1..26.

Formula

a(n) = (1/5)[n*F(2n+2) - n*F(2n-2) + F(2n-1) - (-1)^n], F(n)=A000045(n).

O.g.f.: x*(1-2*x+2*x^2)/((1-3*x+x^2)^2*(1+x)). See the comment above. - Wolfdieter Lang, Jan 02 2012

Crossrefs

Cf. A027926, A024458, A201204, A007598.

Sequence in context: A061136 A308648 A247002 * A120304 A289652 A026071

Adjacent sequences: A027988 A027989 A027990 * A027992 A027993 A027994

Keyword

nonn

Author

Clark Kimberling

Status

approved