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Search: id:A055252
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| 1, 4, 1, 13, 5, 1, 38, 18, 6, 1, 104, 56, 24, 7, 1, 272, 160, 80, 31, 8, 1, 688, 432, 240, 111, 39, 9, 1, 1696, 1120, 672, 351, 150, 48, 10, 1, 4096, 2816, 1792, 1023, 501, 198, 58, 11, 1, 9728, 6912, 4608, 2815, 1524, 699, 256, 69, 12, 1, 22784, 16640, 11520
(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)^2)/(1-2*z)^3)/(1-x*z/(1-z)).
This is the third 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 as A049611(n+1), A001793, A001788, A055580, A055581, A055582, A055583 for m=0..6.
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FORMULA
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a(n, m)=sum(A055249(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)+ A055249(n, m), n >= m >= 0, a(n, m) := 0 if n<m.
G.f. for column m: (((1-x)^2)/(1-2*x)^3)*(x/(1-x))^m, m >= 0.
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EXAMPLE
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{1}; {4,1}; {13,5,1}; {38,18,6,1};...
Fourth row polynomial (n=3): p(3,x)= 38+18*x+6*x^2+x^3
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CROSSREFS
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Cf. A007318, A055248, A055249. Row sums: A049612(n+1)= A055584(n, 0).
Sequence in context: A135704 A002564 A019428 this_sequence A116414 A115154 A051928
Adjacent sequences: A055249 A055250 A055251 this_sequence A055253 A055254 A055255
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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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