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A130301 Lower triangular matrix, read by rows: A130296 * A007318, as infinite lower triangular matrices. 5
1, 3, 1, 5, 3, 1, 7, 6, 4, 1, 9, 10, 10, 5, 1, 11, 15, 20, 15, 6, 1, 13, 21, 35, 35, 27, 7, 1, 15, 28, 56, 70, 56, 28, 8, 1, 17, 36, 84, 126, 126, 84, 36, 9, 1, 19, 45, 120, 210, 252, 210, 120, 45, 10, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

Row sums = A083706: (1, 4, 9, 18, 35, 68,...). A130300 = A007318 * A130296.

The lower triangular matrix A130296 is equal to the restriction of the square array A051340 to its lower left triangular part. So this is also equal to (A051340) * A007318, where (A051340) is the lower triangular part of A051340, i.e., A051340[i,j] replaced by zero for j>i: see  Mathar's Maple code. - M. F. Hasler, Aug 15 2015

LINKS

Table of n, a(n) for n=1..55.

FORMULA

A130296 * A007318 as infinite lower triangular matrices.

A130301[m,n] = A121775[m,n] for n >= m/2. A130301[m,1] = 2m-1, A130301[m,2] = A000217[m-1], A130301[m,m] = 1, A130301[m,m-1] = m for m>2. - M. F. Hasler, Aug 15 2015

EXAMPLE

First few rows of the triangle are:

1;

3, 1;

5, 3, 1;

7, 6, 4, 1;

9, 10, 10, 5, 1;

11, 15, 20, 15, 6, 1;

13, 21, 35, 35, 21, 7, 1;

...

MAPLE

A130301 := proc(n, k)

    add( A051340(n, i)*binomial(i, k), i=k..n);

end proc: # R. J. Mathar, Jul 16 2015

CROSSREFS

Cf. A130296, A130300, A083706.

Sequence in context: A147754 A084305 A099375 * A133601 A258207 A133094

Adjacent sequences:  A130298 A130299 A130300 * A130302 A130303 A130304

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, May 20 2007

EXTENSIONS

Corrected (missing a(15)=1 inserted) by M. F. Hasler, Aug 15 2015

STATUS

approved

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Last modified August 15 13:27 EDT 2020. Contains 336504 sequences. (Running on oeis4.)