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A187887
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Riordan matrix (1/((1-x)*sqrt(1-4*x)),x/(1-x)).
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2
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1, 3, 1, 9, 4, 1, 29, 13, 5, 1, 99, 42, 18, 6, 1, 351, 141, 60, 24, 7, 1, 1275, 492, 201, 84, 31, 8, 1, 4707, 1767, 693, 285, 115, 39, 9, 1, 17577, 6474, 2460, 978, 400, 154, 48, 10, 1, 66197, 24051, 8934, 3438, 1378, 554, 202, 58, 11, 1, 250953, 90248, 32985, 12372, 4816, 1932, 756, 260, 69, 12, 1
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OFFSET
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0,2
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COMMENTS
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LINKS
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FORMULA
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a(n,k) = [x^n] 1/((1-x)*sqrt(1-4*x))*(x/(1-x))^k.
Recurrence: a(n+1,k+1) = a(n,k+1) + a(n,k).
a(n,k) = sum(binomial(n-i,k)*binomial(2*i,i),i=0..n).
G.f.: 1/(sqrt(1-4*x)*(1-x-x*y)).
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EXAMPLE
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Triangle begins:
1,
3,1,
9,4,1,
29,13,5,1,
99,42,18,6,1,
351,141,60,24,7,1,
1275,492,201,84,31,8,1,
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MATHEMATICA
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Select[Flatten[Table[Sum[Binomial[n-i, k]Binomial[2i, i], {i, 0, n}], {n, 0, 10}, {k, 0, 10}]], #!=0&] (* Harvey P. Dale, Jul 05 2012 *)
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PROG
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(Maxima) create_list(sum(binomial(n-i, k)*binomial(2*i, i), i, 0, n), n, 0, 8, k, 0, n);
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CROSSREFS
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KEYWORD
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AUTHOR
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EXTENSIONS
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Comment added and comment corrected by Michel Marcus, Jun 23 2013
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STATUS
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approved
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