The On-Line Encyclopedia of Integer Sequences (OEIS)

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A111993

Fifth convolution of Schroeder's (second problem) numbers A001003(n), n>=0.
(history; published version)

#13 by N. J. A. Sloane at Fri Mar 17 00:47:12 EDT 2017

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proposed

approved

#12 by G. C. Greubel at Thu Mar 16 23:43:57 EDT 2017

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editing

proposed

#11 by G. C. Greubel at Thu Mar 16 23:43:45 EDT 2017

FORMULA

a(n)= (5/n)*sum(Sum_{k=1,..,n} binomial(n, k)*binomial(n+k+4, k-1), k=1..n) = 5*hypergeom([1-n, n+6], [2], -1), n>=1, a(0)=1.

a(n) = 5*hypergeom([1-n, n+6], [2], -1), n>=1, a(0)=1.

PROG

(PARI) x='x+O('x^50); Vec(((1+x-sqrt(1-6*x+x^2))/(4*x))^5) \\ G. C. Greubel, Mar 16 2017

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approved

editing

#10 by Joerg Arndt at Sat May 18 09:10:58 EDT 2013

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proposed

approved

#9 by Vincenzo Librandi at Sat May 18 02:59:07 EDT 2013

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editing

proposed

#8 by Vincenzo Librandi at Sat May 18 02:58:57 EDT 2013

LINKS

Vincenzo Librandi, <a href="/A111993/b111993.txt">Table of n, a(n) for n = 0..300</a>

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approved

editing

#7 by Joerg Arndt at Thu Oct 18 10:45:33 EDT 2012

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proposed

approved

#6 by Vaclav Kotesovec at Thu Oct 18 09:23:28 EDT 2012

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editing

proposed

#5 by Vaclav Kotesovec at Thu Oct 18 09:23:20 EDT 2012

FORMULA

Recurrence: n*(n+5)*a(n) = n*(7*n+23)*a(n-1) - (n+2)*(7*n-9)*a(n-2) + (n-3)*(n+2)*a(n-3). - Vaclav Kotesovec, Oct 18 2012

a(n) ~ 5*sqrt(3*sqrt(2)-4)*(17-12*sqrt(2)) * (3+2*sqrt(2))^(n+5)/(16*sqrt(Pi)*n^(3/2)). - Vaclav Kotesovec, Oct 18 2012

MATHEMATICA

CoefficientList[Series[((1+x-Sqrt[1-6*x+x^2])/(4*x))^5, {x, 0, 20}], x] (* Vaclav Kotesovec, Oct 18 2012 *)

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approved

editing

#4 by Charles R Greathouse IV at Fri Oct 12 14:40:24 EDT 2012

AUTHOR

Wolfdieter Lang (wolfdieter.lang_AT_physik_DOT_uni-karlsruhe_DOT_de), Sep 12 2005

Wolfdieter Lang, Sep 12 2005

Discussion

Fri Oct 12

14:40

OEIS Server: https://oeis.org/edit/global/1838