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A119578 a(n) = (n + n^2)*binomial(2*n,n)/2. 2
0, 2, 18, 120, 700, 3780, 19404, 96096, 463320, 2187900, 10161580, 46558512, 210924168, 946454600, 4212243000, 18614102400, 81746933040, 357041751660, 1551848136300, 6715600122000, 28947771052200, 124337568995640 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

For n > 0, also the number of one-sided prudent walks from (0,0) to (n,n), with n+2 east steps, 2 west steps and n north steps.

REFERENCES

S. Gao, H. Niederhausen, Sequences Arising From Prudent Self-Avoiding Walks (submitted to INTEGERS: The Electronic Journal of Combinatorial Number Theory).

LINKS

Bruno Berselli, Table of n, a(n) for n = 0..500

Shanzhen Gao, Keh-Hsun Chen, Tackling Sequences From Prudent Self-Avoiding Walks, FCS'14, The 2014 International Conference on Foundations of Computer Science.

FORMULA

a(n) = (n+1)*Gamma(2*n)/Gamma(n)^2 for n > 0. - Shanzhen Gao, Apr 26 2011

MAPLE

[seq ((n+n^2)*(binomial(2*n, n))/2, n=0..29)];

MATHEMATICA

Table[(n+n^2) Binomial[2n, n]/2, {n, 0, 30}] (* Harvey P. Dale, Jun 02 2016 *)

PROG

(MAGMA) [0] cat [ (n+1)*Factorial(2*n-1)/Factorial(n-1)^2: n in [1..23] ]; // Klaus Brockhaus, Apr 30 2011

CROSSREFS

Cf. A000984.

Sequence in context: A153338 A007798 A058052 * A052610 A052653 A289830

Adjacent sequences:  A119575 A119576 A119577 * A119579 A119580 A119581

KEYWORD

nonn,easy

AUTHOR

Zerinvary Lajos, May 31 2006

STATUS

approved

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Last modified August 20 10:41 EDT 2019. Contains 326150 sequences. (Running on oeis4.)