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A232969 The sequence S(n,n) that enumerates a certain class of lattice paths from (0,0) to (n,n). 2
1, 6, 60, 675, 7992, 97416, 1209951, 15227190, 193507056, 2477564820, 31910429520, 412987306320, 5366341375695, 69965422235442, 914825583252396, 11991475839917115, 157524763370404320, 2073261181622482080, 27333449595845251524, 360903785815145617992 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

See Dziemianczuk for precise definition.

LINKS

Lars Blomberg, Table of n, a(n) for n = 0..100

M. Dziemianczuk, Counting Lattice Paths With Four Types of Steps, Graphs and Combinatorics, September 2013, DOI 10.1007/s00373-013-1357-1.

MATHEMATICA

Table[Function[k, Sum[Sum[Binomial[k, j] Binomial[j, i - j] Binomial[2 k + n - i, k], {j, 0, i}], {i, 0, n + k}]]@ n, {n, 0, 19}] (* Michael De Vlieger, Jul 22 2017 *)

PROG

(PARI) \\ Dziemianczuk, Proposition 1

S(n, k)=sum(i=0, n+k, sum(j=0, i, binomial(k, j)*binomial(j, i-j)*binomial(2*k+n-i, k)));

vector(20, x, x--; S(x, x)) \\ Lars Blomberg, Jul 20 2017

CROSSREFS

Leading column of array in A232973.

Sequence in context: A106259 A085364 A228484 * A232246 A086984 A000894

Adjacent sequences:  A232966 A232967 A232968 * A232970 A232971 A232972

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Dec 05 2013

EXTENSIONS

a(8)-a(19) from Lars Blomberg, Jul 20 2017

STATUS

approved

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Last modified February 21 06:40 EST 2019. Contains 320371 sequences. (Running on oeis4.)