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Search: id:A072547
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| A072547 |
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Main diagonal of the array in which first column and row are filled alternatively with 1's or 0's and then T(i,j)=T(i-1,j)+T(i,j-1). |
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+0
7
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| 1, 0, 2, 6, 22, 80, 296, 1106, 4166, 15792, 60172, 230252, 884236, 3406104, 13154948, 50922986, 197519942, 767502944, 2987013068, 11641557716, 45429853652, 177490745984, 694175171648, 2717578296116, 10648297329692, 41757352712480
(list; graph; listen)
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OFFSET
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1,3
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COMMENT
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A Catalan transform of A078008 under the mapping g(x)->g(xc(x)). - Paul Barry (pbarry(AT)wit.ie), Nov 13 2004
a(n) = A108561(2*(n-1),n-1). - Reinhard Zumkeller (reinhard.zumkeller(AT)gmail.com), Jun 10 2005
Number of positive terms in expansion of (x_1+x_2+...+x_{n-1}-x_n)^n. - Sergio Falcon (sfalcon(AT)dma.ulpgc.es), Feb 08 2007
Hankel transform is A088138(n+1). [From Paul Barry (pbarry(AT)wit.ie), Feb 17 2009]
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REFERENCES
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Paul Barry, A Catalan Transform and Related Transformations on Integer Sequences, Journal of Integer Sequences, Vol. 8 (2005), Article 05.4.5.
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FORMULA
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If offset is 0, a(n) = Sum_{k=0..n} (-1)^(n-k)*binomial(n+k-1, k). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 18 2003
G.f.: x*(1-x*C)/(1-2*x*C)/(1+x*C), where C = (1-(1-4*x)^(1/2))/x/2 is g.f. for Catalan numbers (A000108). - Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 18 2003
a(n)=sum(binomial(2n-2j-4, n-3), j=0..floor((n-1)/2)). - Emeric Deutsch (deutsch(AT)duke.poly.edu), Jan 28 2004
a(n)=(-1)^n*sum{k=0..n, C(-n,k)} (offset 0). [From Paul Barry (pbarry(AT)wit.ie), Feb 17 2009]
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EXAMPLE
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The array begins:
1 0 1 0 1..
0 0 1 1 2..
1 1 2 3 5..
0 1 3 6 11..
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CROSSREFS
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Cf. A014300, A026641, A092785.
Sequence in context: A148496 A106434 A150228 this_sequence A150229 A150230 A150231
Adjacent sequences: A072544 A072545 A072546 this_sequence A072548 A072549 A072550
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KEYWORD
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nonn
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AUTHOR
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Benoit Cloitre (benoit7848c(AT)orange.fr), Aug 05 2002
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EXTENSIONS
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Corrected and extended by Vladeta Jovovic (vladeta(AT)eunet.rs), Feb 17 2003
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