The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A100192 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A100192

a(n) = Sum_{k=0..n} binomial(2n,n+k)*2^k.
(history; published version)

#20 by Susanna Cuyler at Thu Oct 12 22:17:50 EDT 2017

STATUS

proposed

approved

#19 by Michel Marcus at Thu Oct 12 12:40:00 EDT 2017

STATUS

editing

proposed

#18 by Michel Marcus at Thu Oct 12 12:39:51 EDT 2017

COMMENTS

A transform of 2^n under the mapping g(x)->(1/sqrt(1-4x))g(xc(x)^2), where c(x) is the g.f. of the Catalan numbers A000108. A transform of 3^n under the mapping g(x)->(1/(c(x)*sqrt(1-4x))g(xcx*c(x)).

STATUS

proposed

editing

#17 by Ilya Gutkovskiy at Thu Oct 12 12:29:16 EDT 2017

STATUS

editing

proposed

#16 by Ilya Gutkovskiy at Thu Oct 12 12:06:15 EDT 2017

NAME

a(n) = Sum _{k=0..n} binomial(2n,n+k)*2^k, k=0..n.

FORMULA

a(n) = [x^n] 1/((1 - x)^n*(1 - 3*x)). - Ilya Gutkovskiy, Oct 12 2017

STATUS

approved

editing

#15 by Joerg Arndt at Thu Feb 13 03:30:59 EST 2014

STATUS

reviewed

approved

#14 by Bruno Berselli at Thu Feb 13 03:14:47 EST 2014

STATUS

proposed

reviewed

#13 by Bruno Berselli at Thu Feb 13 03:14:43 EST 2014

STATUS

editing

proposed

#12 by Bruno Berselli at Thu Feb 13 03:14:38 EST 2014

FORMULA

G.f.: (sqrt(1-4x)+1)/(sqrt(1-4x)(3sqrt(1-4x)-1)); G.f.: sqrt(1-4x)(sqrt(1-4x)-3x+1)/((1-4x)(2-9x)); a(n)=sum{k=0..n, binomial(2n, n-k)2^k}.

G.f.: (sqrt(1-4*x)+1)/(sqrt(1-4*x)*(3*sqrt(1-4*x)-1)).

G.f.: sqrt(1-4*x)*(sqrt(1-4*x)-3*x+1)/((1-4*x)*(2-9*x)).

a(n) = sum{k=0..n, Cbinomial(2n, n-k)*2^(n-k)}; - _Paul Barry_, Jan 11 2007.

a(n) = sum{k=0..n, C(n+k-1,2n,k)3*2^(n-k)}; - Paul Barry, Sep 28 Jan 11 2007

a(n) = sum{k=0..n, C(n+k-1,k)3^(n-k)}; - Paul Barry, Sep 28 2007

STATUS

proposed

editing

#11 by Vincenzo Librandi at Thu Feb 13 03:12:41 EST 2014

STATUS

editing

proposed