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Search: id:A054336
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| A054336 |
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A convolution triangle of numbers based on A001405 (central binomial coefficients). |
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+0
7
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| 1, 1, 1, 2, 2, 1, 3, 5, 3, 1, 6, 10, 9, 4, 1, 10, 22, 22, 14, 5, 1, 20, 44, 54, 40, 20, 6, 1, 35, 93, 123, 109, 65, 27, 7, 1, 70, 186, 281, 276, 195, 98, 35, 8, 1, 126, 386, 618, 682, 541, 321, 140, 44, 9, 1, 252, 772, 1362, 1624, 1440, 966, 497, 192, 54, 10, 1
(list; table; graph; listen)
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OFFSET
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0,4
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COMMENT
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In the language of the Shapiro et al. reference (given in A053121) such a lower triangular (ordinary) convolution array, considered as a matrix, belongs to the Bell-subgroup of the Riordan-group.
The G.f. for the row polynomials p(n,x) (increasing powers of x) is 1/(1-(1+x)*z-z^2*c(z^2)), with c(x) the g.f. for Catalan numbers A000108.
Column sequences: A001405, A045621.
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FORMULA
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G.f. for column m: cbi(x)*(x*cbi(x))^m, with cbi(x) := (1+x*c(x^2))/sqrt(1-4*x^2) = 1/(1-x-x^2*c(x^2)), where c(x) is the g.f. for Catalan numbers A000108.
T(n,k)=Sum_{j, j>=0}A053121(n,j)*binomial(j,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), Mar 30 2007
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EXAMPLE
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{1}; {1,1}; {2,2,1}; {3,5,3,1};...
Fourth row polynomial (n=3): p(3,x)= 3+5*x+3*x^2+x^3
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CROSSREFS
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Cf. A001405, A035324, A054335 . Row sums: A054341(n).
Sequence in context: A037027 A139375 A106198 this_sequence A079956 A026300 A099514
Adjacent sequences: A054333 A054334 A054335 this_sequence A054337 A054338 A054339
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KEYWORD
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easy,nice,nonn,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Mar 13 2000
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