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A189770 Number of one-sided prudent walks from (0,0) to (n,n), with 4+n east steps, 4 west steps and n north steps. 1
2, 30, 300, 2450, 17640, 116424, 720720, 4247100, 24066900, 132100540, 706137432, 3691172940, 18929092000, 95477508000, 474659611200, 2329787591640, 11306322135900, 54314684770500, 258550604697000, 1220631012701100, 5719528173799440, 26616851891058000 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,1

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 1..150

S. Gao and H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks, 2010.

FORMULA

a(n) = (n+1)(2+n)(n+3) Gamma(1+2n) / (24n(Gamma(n))^2).

MATHEMATICA

Table[(n+1)*(2+n)*(n+3)*Gamma[1+2*n]/(24*n*(Gamma[n])^2), {n, 30}]

PROG

(MAGMA) [ Round((n+1)*(n+2)*(n+3)*Gamma(1+2*n)/(24*n*Gamma(n)^2)): n in [1..22] ]; // Klaus Brockhaus, Apr 29 2011

CROSSREFS

Sequence in context: A300608 A301350 A036351 * A245020 A277660 A089433

Adjacent sequences:  A189767 A189768 A189769 * A189771 A189772 A189773

KEYWORD

nonn,walk

AUTHOR

Shanzhen Gao, Apr 26 2011

STATUS

approved

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Last modified January 25 23:56 EST 2022. Contains 350572 sequences. (Running on oeis4.)