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A026302
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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.
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2
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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; internal format)
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OFFSET
| 0,2
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FORMULA
| a(n) = binomial(2*n,n)*hypergeom([ -n/2, 1/2 - n/2],[n+2],4) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jun 02 2010]
A026302(n) = (n + 1) * A006605(n) [From Mark van Hoeij (hoeij(AT)math.fsu.edu), Jul 02 2010]
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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))) ; }
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CROSSREFS
| Bisection of A026307.
Sequence in context: A199308 A176479 A162356 * A124889 A108308 A119855
Adjacent sequences: A026299 A026300 A026301 * A026303 A026304 A026305
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KEYWORD
| nonn
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AUTHOR
| Clark Kimberling (ck6(AT)evansville.edu)
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EXTENSIONS
| Corrected by R. J. Mathar, Oct 26 2006
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