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A135089 T(n,k) = 5*binomial(n,k), n>0, (0<=k<=n). 2
1, 5, 5, 5, 10, 5, 5, 15, 15, 5, 5, 20, 30, 20, 5, 5, 25, 50, 50, 25, 5, 5, 30, 75, 100, 75, 30, 5, 5, 35, 105, 175, 175, 105, 35, 5, 5, 40, 140, 280, 350, 280, 140, 40, 5, 5, 45, 180, 420, 630, 630, 420, 180, 45, 5, 5, 50, 225, 600, 1050, 1260, 1050, 600, 225, 50, 5 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Row sums = A020714 (except for the first term).

REFERENCES

Triangle T(n,k), 0<=k<=n, read by rows given by (5, -4, 0, 0, 0, 0, 0, 0, 0...) DELTA (5, -4, 0, 0, 0, 0, 0, 0, 0, ...) where DELTA is the operator defined in A084938. - Philippe Deléham, Nov 24 2013

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows

FORMULA

T(n,k) = 5*binomial (n,k), n>0, (0<=k<=n).

Equals 2*A134059 - A007318.

G.f.: (1+4*x+4*x*y)/(1-x-x*y). - Philippe Deléham, Nov 24 2013

EXAMPLE

First few rows of the triangle are:

1;

5, 5;

5, 10, 5;

5, 15, 15, 5;

5, 20, 30 20, 5;

5, 25, 50, 50, 25, 5;

5, 30, 75, 100, 75, 30, 5.

MATHEMATICA

Join[{1}, Table[5*Binomial[n, k], {n, 1, 10}, {k, 0, n}]] // Flatten (* G. C. Greubel, Sep 22 2016 *)

CROSSREFS

Cf. A007318, A134058, A134059, A132200, A020714.

Sequence in context: A087516 A194428 A299695 * A127310 A214925 A101597

Adjacent sequences:  A135086 A135087 A135088 * A135090 A135091 A135092

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Nov 18 2007

STATUS

approved

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Last modified September 23 18:51 EDT 2020. Contains 337315 sequences. (Running on oeis4.)