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A026302 a(n) = number of (s(0), s(1), ..., s(n)) such that s(i) is a nonnegative integer and |s(i) - s(i-1)| <= 1 for i = 1,2,...,n, s(0) = 0, s(2n) = n. Also a(n) = T(2n,n), where T is the array in A026300. 2
1, 2, 9, 44, 230, 1242, 6853, 38376, 217242, 1239980, 7123765, 41141916, 238637282, 1389206210, 8112107475, 47495492400, 278722764954, 1638970147188, 9654874654438, 56965811111240, 336590781348276, 1991357644501170 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

REFERENCES

D. Kruchinin and V. Kruchinin, A Method for Obtaining Generating Function for Central Coefficients of Triangles, Journal of Integer Sequence,  Vol. 15 (2012), article 12.9.3.

LINKS

Table of n, a(n) for n=0..21.

FORMULA

a(n) = binomial(2*n,n)*hypergeom([ -n/2, 1/2 - n/2],[n+2],4). - Mark van Hoeij, Jun 02 2010

a(n) = (n + 1) * A006605(n). - Mark van Hoeij, Jul 02 2010

G.f. A(x)=(x*M(x))', where M(x)=1+x*M(x)^2+x^2*M(x)^4. - Vladimir Kruchinin, May 25 2012

From Ilya Gutkovskiy, Sep 21 2017: (Start)

a(n) = [x^n] ((1 - x - sqrt(1 - 2*x - 3*x^2))/(2*x^2))^(n+1).

a(n) = [x^n] (1/(1 - x - x^2/(1 - x - x^2/(1 - x - x^2/(1 - x - x^2/(1 - x - x^2/(1 - ...)))))))^(n+1), a continued fraction. (End)

PROG

(PARI programs from R. J. Mathar) A026300(n, k)={ if(n<0 || k < 0, return(0) ; ) ; if(n<=1, 1, if(k==0, 1, sum(i=0, k/2, binomial(n, 2*i+n-k)*(binomial(2*i+n-k, i)-binomial(2*i+n-k, i-1))) ; ) ; ) ; }

A026302(n)={ A026300(2*n, n) ; } { for(n=0, 21, print(n, " ", A026302(n))) ; }

CROSSREFS

Bisection of A026307.

Sequence in context: A199308 A176479 A162356 * A214460 A124889 A295809

Adjacent sequences:  A026299 A026300 A026301 * A026303 A026304 A026305

KEYWORD

nonn

AUTHOR

Clark Kimberling

EXTENSIONS

Corrected by R. J. Mathar, Oct 26 2006

STATUS

approved

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Last modified February 24 18:24 EST 2018. Contains 299628 sequences. (Running on oeis4.)