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A055584 Triangle of partial row sums (prs) of triangle A055252. 5
1, 5, 1, 19, 6, 1, 63, 25, 7, 1, 192, 88, 32, 8, 1, 552, 280, 120, 40, 9, 1, 1520, 832, 400, 160, 49, 10, 1, 4048, 2352, 1232, 560, 209, 59, 11, 1, 10496, 6400, 3584, 1792, 769, 268, 70, 12, 1, 26624, 16896, 9984, 5376, 2561, 1037, 338, 82, 13, 1, 66304, 43520 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

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)^3)/(1-2*z)^4)/(1-x*z/(1-z)).

This is the fourth 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 A049612(n+1), A055585, A001794, A001789(n+3), A027608, A055586 for m=0..5.

LINKS

Table of n, a(n) for n=0..56.

FORMULA

a(n, m)=sum(A055252(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)+ A055252(n, m), n >= m >= 0, a(n, m) := 0 if n<m.

G.f. for column m: (((1-x)^3)/(1-2*x)^4)*(x/(1-x))^m, m >= 0.

EXAMPLE

{1}; {5,1}; {19,6,1}; {63,25,7,1};...

Fourth row polynomial (n=3): p(3,x)= 63+25*x+7*x^2+x^3

CROSSREFS

Cf. A007318, A055248, A055249, A055252. Row sums: A049600(n+1, 4).

Sequence in context: A151335 A297174 A226605 * A193861 A193857 A146055

Adjacent sequences:  A055581 A055582 A055583 * A055585 A055586 A055587

KEYWORD

easy,nonn,tabl

AUTHOR

Wolfdieter Lang, May 26 2000

STATUS

approved

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Last modified April 22 04:04 EDT 2019. Contains 322329 sequences. (Running on oeis4.)