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A242233 2^n*(C_n)^(1/2) in the Cauchy type product where C_n is the n-th Catalan number. 1
1, 1, 3, 11, 41, 137, 347, 611, 5777, 98321, 677363, -4192197, -134908871, -617972327, 22749265099, 449951818387, -632325203423, -163681108703199, -2324079456844573, 33233931805782635, 1734259111955765577, 14135975420529458857, -777499293367428199109 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..22.

FORMULA

a(n) = 2^n*n!*[x^n](sqrt(exp(2*x)*(BesselI(0,2*x)-BesselI(1,2*x)))), where [x^n](f(x)) the coefficient of x^n in f(x).

MAPLE

f := sqrt(exp(2*x)*(BesselI(0, 2*x)-BesselI(1, 2*x)));

seq(2^n*n!*coeff(series(f, x, n+1), x, n), n=0..22);

# Second program with function g from A241885:

catalan := n -> binomial(2*n, n)/(n+1);

a := n -> 2^n*g(catalan, n); seq(a(n), n=0..22);

MATHEMATICA

g[n_] := g[n] = (CatalanNumber[n] - Sum[Binomial[n, m] g[m] g[n - m], {m, 1, n - 1}])/2;

a[0] = 1; a[n_] := 2^n g[n];

Table[a[n], {n, 0, 22}] (* Jean-Fran├žois Alcover, Aug 02 2019, from 2nd Maple program *)

CROSSREFS

Cf. A126156, A241885.

Sequence in context: A073622 A181863 A075276 * A294504 A086972 A218348

Adjacent sequences:  A242230 A242231 A242232 * A242234 A242235 A242236

KEYWORD

sign

AUTHOR

Peter Luschny, May 08 2014

STATUS

approved

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Last modified January 22 22:16 EST 2020. Contains 331166 sequences. (Running on oeis4.)