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Search: id:A055249
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| 1, 3, 1, 8, 4, 1, 20, 12, 5, 1, 48, 32, 17, 6, 1, 112, 80, 49, 23, 7, 1, 256, 192, 129, 72, 30, 8, 1, 576, 448, 321, 201, 102, 38, 9, 1, 1280, 1024, 769, 522, 303, 140, 47, 10, 1, 2816, 2304, 1793, 1291, 825, 443, 187, 57, 11, 1, 6144, 5120, 4097, 3084, 2116, 1268, 630
(list; table; graph; listen)
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OFFSET
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0,2
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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 matrix, belongs to the Riordan-group. The G.f. for the row polynomials p(n,x) (increasing powers of x) is ((1-z)/(1-2*z)^2)/(1-x*z/(1-z)).
This is the second member of the family of Riordan-type matrices obtained from A007318(n,m) (Pascal's triangle read as lower triangular matrix) by repeated application of the prs-procedure.
The column sequences appear in A001792, A001787, A000337, A045618, A045889, A034009, A055250, A055251 for m=0..7.
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FORMULA
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a(n, m)=sum(A055248(n, k), k=m..n), n >= m >= 0, a(n, m) := 0 if n<m, (sequence of partial row sums in column m).
Column m recursion: a(n, m)= sum(a(j, m), j=m..n-1)+ A055248(n, m), n >= m >= 0, a(n, m) := 0 if n<m.
G.f. for column m: ((1-x)/(1-2*x)^2)*(x/(1-x))^m, m >= 0.
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EXAMPLE
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{1}; {3,1}; {8,4,1}; {20,12,5,1};...
Fourth row polynomial (n=3): p(3,x)= 20+12*x+5*x^2+x^3
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CROSSREFS
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Cf. A007318, A055248, A008949. Row sums: A049611(n+1) = A055252(n, 0).
Sequence in context: A065451 A054506 A101026 this_sequence A125172 A073732 A021318
Adjacent sequences: A055246 A055247 A055248 this_sequence A055250 A055251 A055252
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KEYWORD
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easy,nonn,tabl
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AUTHOR
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Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), May 26 2000
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