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Search: id:A081577
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| 1, 1, 1, 1, 4, 1, 1, 7, 7, 1, 1, 10, 22, 10, 1, 1, 13, 46, 46, 13, 1, 1, 16, 79, 136, 79, 16, 1, 1, 19, 121, 307, 307, 121, 19, 1, 1, 22, 172, 586, 886, 586, 172, 22, 1, 1, 25, 232, 1000, 2086, 2086, 1000, 232, 25, 1, 1, 28, 301, 1576, 4258, 5944, 4258, 1576, 301, 28, 1
(list; table; graph; listen)
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OFFSET
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0,5
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COMMENT
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One of a family of Pascal-like arrays. A007318 is equivalent to the (1,0,1)-array. A008288 is equivalent to the (1,1,1)-array. Rows include A016777, A038764, A081583, A081584. Coefficients of the row polynomials in the Newton basis are given by A013610.
As a number triangle, this is the Riordan array (1/(1-x), x(1+2x)/(1-x)). It has row sums A002605 and diagonal sums A077947. - Paul Barry (pbarry(AT)wit.ie), Jan 24 2005
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REFERENCES
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Paul Barry, On Integer-Sequence-Based Constructions of Generalized Pascal Triangles, Journal of Integer Sequences, Vol. 9 (2006), Article 06.2.4.
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FORMULA
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Square array T(n, k) defined by T(n, 0)=T(0, k)=1, T(n, k)=T(n, k-1)+2T(n-1, k-1)+T(n-1, k). Rows are the expansions of (1+2x)^k/(1-x)^(k+1).
G.f.: 1/(1-x-y-2xy). - Ralf Stephan, Apr 28 2004
T(n,k)=sum{j=0..n, C(k,j-k)*C(n+k-j,k)*2^(j-k)}; - Paul Barry (pbarry(AT)wit.ie), Oct 23 2006
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EXAMPLE
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Rows begin
1 1 1 1 1 ...
1 4 7 10 13 ...
1 7 22 46 79 ...
1 10 46 136 307 ...
1 13 79 307 886 ...
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CROSSREFS
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Cf. A081578, A081579, A081580.
Adjacent sequences: A081574 A081575 A081576 this_sequence A081578 A081579 A081580
Sequence in context: A131060 A124376 A047671 this_sequence A073697 A119673 A051455
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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), Mar 23 2003
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