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Search: id:A094531
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| A094531 |
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Array read by rows: right-hand side of triangle A027907 of trinomial coefficients. |
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+0
5
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| 1, 1, 1, 3, 2, 1, 7, 6, 3, 1, 19, 16, 10, 4, 1, 51, 45, 30, 15, 5, 1, 141, 126, 90, 50, 21, 6, 1, 393, 357, 266, 161, 77, 28, 7, 1, 1107, 1016, 784, 504, 266, 112, 36, 8, 1, 3139, 2907, 2304, 1554, 882, 414, 156, 45, 9, 1, 8953, 8350, 6765, 4740, 2850, 1452, 615, 210, 55
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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Expand (1+x+x^2)^n and take last (nonzero) coefficient of first row, last two coefficients of second row, etc.
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REFERENCES
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L. W. Shapiro, S. Getu, W.-J. Woan and L. C. Woodson, The Riordan group, Discrete Applied Math., 34 (1991), 229-239.
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FORMULA
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Riordan array ( 1/sqrt(1-2*x-3*x^2), (1-x-sqrt(1-2*x-3*x^2))/(2*x) ). - njas, Jun 02 2005
Product of Riordan arrays (1/(1-x), x/(1-x)) (Pascal's triangle, A007318) and (1/sqrt(1-4x^2), (1-sqrt(1-4*x^2))/(2*x)) (A108044). Inverse is A102587. - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
Column k has e.g.f. exp(x)Bessel_I(k, 2x); - Paul Barry (pbarry(AT)wit.ie), Jul 14 2005
T(n, k)=sum{i=0..n, C(n-k-i, i)C(n, k+i)}. - Paul Barry (pbarry(AT)wit.ie), Nov 04 2005
T(n,k)=sum{j=0..n, C(n,j)*C(j,n-k-j)}; - Paul Barry (pbarry(AT)wit.ie), Oct 25 2006
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EXAMPLE
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Rows start {1}, {1,1}, {3,2,1}, {7,6,3,1},...
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CROSSREFS
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Binomial transform is triangle A094527. Row sums are A027914.
Adjacent sequences: A094528 A094529 A094530 this_sequence A094532 A094533 A094534
Sequence in context: A105531 A129689 A115990 this_sequence A111960 A130462 A059380
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Paul Barry (pbarry(AT)wit.ie), May 07 2004
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