A155051 Expansion of c(x^2)*(1+x)/(1-x), c(x) the g.f. of A000108.

1, 2, 3, 4, 6, 8, 13, 18, 32, 46, 88, 130, 262, 394, 823, 1252, 2682, 4112, 8974, 13836, 30632, 47428, 106214, 165000, 373012, 581024, 1323924, 2066824, 4741264, 7415704, 17110549, 26805394, 62163064, 97520734, 227165524

Offset

0,2

Comments

Row sums of A155050.

Conjecture: A000975(n) = A264784(a(n-1)) for n > 0. - Reinhard Zumkeller, Dec 04 2015

Links

G. C. Greubel, Table of n, a(n) for n = 0..1000

Formula

a(n) = 2*Sum_{k=0..n,} ( C(k/2)*(1+(-1)^k)/2 ) - C(n/2)*(1+(-1)^n)/2, C(n) = A000108;

a(n) = (C(n/2) + 2*Sum_{k=0..(n/2-1), C(k)})*(1+(-1)^n)/2 + Sum_{k=0..n/2, C(k)}*(1-(-1)^n), C(n) = A000108.

Conjecture: (n+2)*a(n) -2*a(n-1) +(-5*n+4)*a(n-2) +8*a(n-3) +4*(n-3)*a(n-4)=0. - R. J. Mathar, Feb 05 2015

Conjecture: -(n+2)*(n-3)*a(n) +(n^2-n-10)*a(n-1) +4*(n^2-4*n+5)*a(n-2) -4*(n-2)^2*a(n-3)=0. - R. J. Mathar, Feb 05 2015

Mathematica

A155051[n_] := 2*Sum[CatalanNumber[k/2]*(1 + (-1)^k)/2, {k, 0, n}] -
CatalanNumber[n/2]*(1 + (-1)^n)/2; Table[A155051[n], {n, 0, 50}] (* G. C. Greubel, Sep 30 2017 *)

Crossrefs

Cf. A000108, A155050, A000975, A264784.

Sequence in context: A263359 A246905 A000029 * A018137 A084239 A283022

Adjacent sequences: A155048 A155049 A155050 * A155052 A155053 A155054

Keyword

easy,nonn

Author

Paul Barry, Jan 19 2009

Status

approved