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A167422 Expansion of (1+x)*c(x), c(x) the g.f. of A000108. 4
1, 2, 3, 7, 19, 56, 174, 561, 1859, 6292, 21658, 75582, 266798, 950912, 3417340, 12369285, 45052515, 165002460, 607283490, 2244901890, 8331383610, 31030387440, 115948830660, 434542177290, 1632963760974, 6151850548776 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A167423.

Apparently a(n) = A071716(n) if n>1. - R. J. Mathar, Nov 12 2009

LINKS

G. C. Greubel, Table of n, a(n) for n = 0..500

Murray Tannock, Equivalence classes of mesh patterns with a dominating pattern, MSc Thesis, Reykjavik Univ., May 2016. See Appendix B2

FORMULA

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

a(0)= 1, a(n) = A005807(n-1) for n>0. - Philippe Deléham, Nov 25 2009

(n+1)*a(n) +(-3*n+1)*a(n-1) +2*(-2*n+5)*a(n-2)=0, for n>2. - R. J. Mathar, Feb 10 2015

-(n+1)*(5*n-6)*a(n) +2*(5*n-1)*(2*n-3)*a(n-1)=0. - R. J. Mathar, Feb 10 2015

The o.g.f. A(x) satisfies [x^n] A(x)^(5*n) = binomial(5*n,2*n) = A001450(n). Cf. A182959. - Peter Bala, Oct 04 2015

MATHEMATICA

Table[If[n < 2, n + 1, Binomial[2 n, n]/(n + 1) + Binomial[2 (n - 1), n - 1]/n], {n, 0, 25}] (* Michael De Vlieger, Oct 05 2015 *)

CoefficientList[Series[(1 + t)*(1 - Sqrt[1 - 4*t])/(2*t), {t, 0, 50}], t] (* G. C. Greubel, Jun 12 2016 *)

PROG

(PARI) a(n) = if (n<2, n+1, binomial(2*n, n)/(n+1) + binomial(2*(n-1), n-1)/n);

vector(50, n, a(n-1)) \\ Altug Alkan, Oct 04 2015

CROSSREFS

Cf. A000108, A001450, A005807, A071716, A167423, A182959.

Sequence in context: A037028 A052919 A005807 * A060276 A025563 A224929

Adjacent sequences:  A167419 A167420 A167421 * A167423 A167424 A167425

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Nov 03 2009

STATUS

approved

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Last modified April 1 05:04 EDT 2020. Contains 333155 sequences. (Running on oeis4.)