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A153337 Number of zig-zag paths from top to bottom of a 2n-1 by 2n-1 square whose color is that of the top right corner 5
1, 4, 24, 136, 720, 3624, 17584, 83024, 383904, 1746280, 7839216, 34812144, 153204064, 669108496, 2903267040, 12526343584, 53779871552, 229895033832, 978965187184, 4154438114480, 17575883030496, 74150192517808 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Indranil Ghosh, Table of n, a(n) for n = 1..1000

Joseph Myers, BMO 2008--2009 Round 1 Problem 1---Generalisation

FORMULA

a(n) = n*2^(2n-2) - 2(n-1)*binomial(2n-2,n-1).

EXAMPLE

a(3) = 3 * 2 ^ (2*3 - 2) - 2* (3 - 1) * binomial(2*3 - 2, 3 - 1) = 24. - Indranil Ghosh, Feb 19 2017

MATHEMATICA

Table[(n)2^(2n-2)-2(n-1) Binomial[2n-2, n-1], {n, 1, 22}] (* Indranil Ghosh, Feb 19 2017 *)

PROG

(Python)

import math

def C(n, r):

....f=math.factorial

....return f(n)/f(r)/f(n-r)

def A153337(n):

....return str(n*2**(2*n-2)-2*(n-1)*C(2*n-2, n-1)) # Indranil Ghosh, Feb 19 2017

(PARI) a(n) = n*2^(2*n-2) - 2*(n-1)*binomial(2*n-2, n-1); \\ Michel Marcus, Feb 19 2017

CROSSREFS

Cf. A102699, A153334, A153335, A153336, A153338.

Sequence in context: A048180 A057391 A071079 * A122690 A183512 A204199

Adjacent sequences:  A153334 A153335 A153336 * A153338 A153339 A153340

KEYWORD

easy,nonn

AUTHOR

Joseph Myers, Dec 24 2008

STATUS

approved

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Last modified June 23 11:32 EDT 2017. Contains 288665 sequences.