The OEIS is supported by the many generous donors to the OEIS Foundation.

 Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 59th year, we have over 358,000 sequences, and we’ve crossed 10,300 citations (which often say “discovered thanks to the OEIS”). Other ways to Give
 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A055834 T(2n,n), where T is the array in A055830. 3
 1, 1, 4, 18, 85, 413, 2044, 10248, 51876, 264550, 1357070, 6994780, 36196706, 187938842, 978599560, 5108177816, 26721644973, 140050505085, 735254208670, 3865837887450, 20353393741065, 107290306033845, 566194674179160, 2990958274811520, 15814562990604300, 83690040760923168 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vincenzo Librandi, Table of n, a(n) for n = 0..1000 FORMULA a(n) = Sum_{k=0..n} binomial(n+k-1,n)*binomial(k,n-k). - Max Alekseyev, Jun 17 2007 Recurrence: 5*(n-1)*n*a(n) = 2*(n-1)*(11*n-3)*a(n-1) + 3*(3*n-5)*(3*n-4)*a(n-2). - Vaclav Kotesovec, Nov 19 2012 a(n) ~ 27^n/5^n*sqrt(2/(15*Pi*n)). - Vaclav Kotesovec, Nov 19 2012 a(n) = A055835(n)/3 for n>=1. - Philippe Deléham, Jan 25 2014 G.f.: x*B'(x)-x*B'(x)/B(x)+B(x), where B(x) is g.f. of A001002. - Vladimir Kruchinin, Sep 20 2015 MAPLE seq( add(binomial(n+k-1, n)*binomial(k, n-k), k=0..n), n=0..30); # G. C. Greubel, Jan 21 2020 MATHEMATICA Table[Sum[Binomial[n+k-1, n]Binomial[k, n-k], {k, 0, n}], {n, 0, 30}] (* Harvey P. Dale, Oct 03 2011 *) PROG (PARI) a(n) = sum(k=0, n, binomial(n+k-1, n)*binomial(k, n-k)); \\ Joerg Arndt, May 06 2013 (Maxima) b(n):= sum(binomial(n+k, k)*binomial(k, n-k), k, ceiling(n/2), n)/(n+1); B(x):= sum(b(i)*x^(i), i, 0, 30); makelist(coeff(taylor(x*diff(B(x), x)-x*diff(B(x), x)/B(x)+B(x), x, 0, 20), x, n), n, 0, 20); /* Vladimir Kruchinin, Sep 21 2015 */ (Magma) [&+[(Binomial(n+k-1, n)*Binomial(k, n-k)): k in [0..n]]: n in [0..30]]; // Vincenzo Librandi, Sep 21 2015 (Sage) [sum(binomial(n+k-1, n)*binomial(k, n-k) for k in (0..n)) for n in (0..30)] # G. C. Greubel, Jan 21 2020 (GAP) List([0..30], n-> Sum([0..n], k-> Binomial(n+k-1, n)*Binomial(k, n-k)) ); # G. C. Greubel, Jan 21 2020 CROSSREFS Cf. A001002, A055830, A055835. Sequence in context: A110166 A046885 A247637 * A079567 A030278 A318217 Adjacent sequences: A055831 A055832 A055833 * A055835 A055836 A055837 KEYWORD nonn,easy AUTHOR Clark Kimberling, May 28 2000 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 2 17:25 EST 2022. Contains 358510 sequences. (Running on oeis4.)