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A155051 Expansion of c(x^2)*(1+x)/(1-x), c(x) the g.f. of A000108. 4
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 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 16:23 EST 2021. Contains 349430 sequences. (Running on oeis4.)