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A114422
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Riordan array (1/sqrt(1-2x-3x^2), M(x)-1) where M(x) is the g.f. of the Motzkin numbers A001006.
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14
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1, 1, 1, 3, 3, 1, 7, 9, 5, 1, 19, 26, 19, 7, 1, 51, 75, 65, 33, 9, 1, 141, 216, 211, 132, 51, 11, 1, 393, 623, 665, 483, 235, 73, 13, 1, 1107, 1800, 2058, 1674, 963, 382, 99, 15, 1, 3139, 5211, 6294, 5598, 3663, 1739, 581, 129, 17, 1, 8953, 15115, 19095, 18261, 13243
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OFFSET
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0,4
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COMMENTS
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First column is central trinomial numbers A002426. Second column is A005774. Third column is A025568. Row sums are A116387. Diagonal sums are A116388. Product of A007318 and A116382. Column k has e.g.f. exp(x)*sum{j=0..k, C(k,j)*Bessel_I(k+j,2x)}.
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LINKS
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Table of n, a(n) for n=0..59.
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FORMULA
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Riordan array (1/sqrt(1-2x-3x^2), (1-x-2x^2-sqrt(1-2x-3x^2))/(2x^2)); Number triangle T(n,k)=sum{j=0..n, C(n,j-k)C(j,n-j)}.
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EXAMPLE
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Triangle begins
1,
1, 1,
3, 3, 1,
7, 9, 5, 1,
19, 26, 19, 7, 1,
51, 75, 65, 33, 9, 1,
141, 216, 211, 132, 51, 11, 1
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CROSSREFS
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Sequence in context: A180735 A116401 A106479 * A127501 A181304 A118408
Adjacent sequences: A114419 A114420 A114421 * A114423 A114424 A114425
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry, Feb 12 2006
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STATUS
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approved
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