This site is supported by donations to The OEIS Foundation.

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A137644 a(n) = Sum_{k=0..n} C(n+k,k)*C(n+k,n-k). 8
 1, 3, 16, 95, 591, 3780, 24620, 162423, 1081780, 7258053, 48982176, 332140328, 2261099491, 15444137880, 105789736896, 726426836103, 4998885106599, 34464824536500, 238017084356680, 1646234203000485, 11401464090042224 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 COMMENTS Number of lattice paths from (0,0) to (n,n) using steps (1,0), (1,1), (0,1), (0,2). [From Eric Werley, Jun 29 2011] LINKS FORMULA a(n)= 3F2( {-n, n+1, n+1}; {1/2, 1})( -(1/4) ) [From Olivier GERARD, Apr 23 2009] G.f. A(x)=F'(x)/(1+F(x)), F(x)=x*(1+F(x))/(1-F(x)-F(x)^2). [From Vladimir Kruchinin, Mar 24 2012] EXAMPLE The triangle of number of lattice paths from (0,0) to (n,k) using steps (1,0), (1,1), (0,1), (0,2) begins: 1; 1, 3; 1, 5, 16; 1, 7, 29, 95; 1, 9, 46, 179, 591; 1, 11, 67, 303, 1140, 3780; 1, 13, 92, 475, 2010, 7405, 24620; 1, 15, 121, 703, 3309, 13427, 48761, 162423; 1, 17, 154, 995, 5161, 22892, 90241, 324317, 1081780; This sequence is the diagonal. [Joerg Arndt, Jul 01, 2011] MATHEMATICA Table[ HypergeometricPFQ[{-n, 1 + n, 1 + n}, {1/2, 1}, -(1/4)], {n, 0, 20}] [From Olivier GERARD, Apr 23 2009] Table[Sum[Binomial[n+k, k]Binomial[n+k, n-k], {k, 0, n}], {n, 0, 20}] (* From Harvey P. Dale, Aug 03 2011 *) PROG (PARI) a(n)=sum(k=0, n, binomial(n+k, k)*binomial(n+k, n-k)) CROSSREFS (PARI) /* same as in A092566 but use */ steps=[[1,0], [1,1], [0,1], [0,2]]; /* Joerg Arndt, Jun 30 2011 */ Sequence in context: A221764 A213229 A074555 * A114174 A181067 A006347 Adjacent sequences:  A137641 A137642 A137643 * A137645 A137646 A137647 KEYWORD nonn AUTHOR Paul D. Hanna, Jan 31 2008 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Transforms | Puzzles | Hot | Classics
Recent Additions | More pages | Superseeker | Maintained by The OEIS Foundation Inc.

Content is available under The OEIS End-User License Agreement .

Last modified May 20 01:05 EDT 2013. Contains 225445 sequences.