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Search: id:A008956
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| A008956 |
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Triangle of central factorial numbers 4^k t(2n+1,2n+1-2k). |
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+0
7
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| 1, 1, 1, 1, 10, 9, 1, 35, 259, 225, 1, 84, 1974, 12916, 11025, 1, 165, 8778, 172810, 1057221, 893025, 1, 286, 28743, 1234948, 21967231, 128816766, 108056025, 1, 455, 77077, 6092515, 230673443, 3841278805, 21878089479, 18261468225, 1, 680
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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T(k,n) is the absolute value of the (2n)-th coefficient in Prod[i=1..2k, x+2i-2k-1 ].
Descending row polynomials in x^2 evaluated at k generate odd coefficients of e.g.f. sin(arcsin(kt)/k): 1, x^2 - 1, 9x^4 - 10x^2 + 1, 225x^6 - 259x^4 + 34x^2 - 1, ... - Ralf Stephan, Jan 16 2005
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REFERENCES
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J. Riordan, Combinatorial Identities, Wiley, 1968, p. 217.
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EXAMPLE
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1; 1,1; 1,10,9; 1,35,259,225; ...
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PROGRAM
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(PARI) T(n, k)=if(n<=0, k==0, (-1)^k*polcoeff(numerator(2^(2*n-1)/sum(j=0, 2*n-1, binomial(2*n-1, j)/(x+2*n-1-2*j))), 2*n-2*k))
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CROSSREFS
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Cf. A008958.
Columns include A000447, A001823. Right-hand columns include A001818, A001824, A001825. Cf. A008955.
Sequence in context: A065691 A038310 A118768 this_sequence A081101 A022966 A023452
Adjacent sequences: A008953 A008954 A008955 this_sequence A008957 A008958 A008959
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KEYWORD
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tabl,nonn,easy
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AUTHOR
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njas
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EXTENSIONS
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More terms from Vladeta Jovovic (vladeta(AT)Eunet.yu), Apr 16 2000
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