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A139524 Triangle T(n,k) read by rows: the coefficient of [x^k] of the polynomial 2*(x+1)^n+2^n in row n, column k. 0
3, 4, 2, 6, 4, 2, 10, 6, 6, 2, 18, 8, 12, 8, 2, 34, 10, 20, 20, 10, 2, 66, 12, 30, 40, 30, 12, 2, 130, 14, 42, 70, 70, 42, 14, 2, 258, 16, 56, 112, 140, 112, 56, 16, 2, 514, 18, 72, 168, 252, 252, 168, 72, 18, 2, 1026, 20, 90, 240, 420, 504, 420, 240, 90, 20, 2 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,1

COMMENTS

Row sums are A007283.

REFERENCES

Advanced Number Theory, Harvey Cohn, Dover Books, 1963, Pages 88-89

LINKS

Table of n, a(n) for n=0..65.

FORMULA

T(n,0) = 2+2^n = A052548(n). T(n,k) = 2*binomial(n,k) = A028326(n,k) if k>0. - R. J. Mathar, Sep 12 2013

EXAMPLE

3;

4, 2;

6, 4, 2;

10, 6, 6, 2;

18, 8, 12, 8, 2;

34, 10, 20, 20, 10, 2;

66, 12, 30, 40, 30, 12, 2;

130, 14, 42, 70, 70, 42, 14, 2;

258, 16, 56, 112, 140, 112, 56, 16, 2;

514, 18, 72, 168, 252, 252, 168, 72, 18, 2;

1026, 20, 90, 240, 420, 504, 420, 240, 90, 20, 2;

MATHEMATICA

Clear[f, x, n] f[x_, y_, n_] = Sum[Binomial[n, i]*x^i*y^(n - i), {i, 0, n}]; Table[ExpandAll[f[x, y, n] + f[y, z, n] + f[x, z, n]], {n, 0, 10}] a = Table[CoefficientList[ExpandAll[f[x, y, n] + f[y, z, n] + f[x, z, n]] /. y -> 1 /. z -> 1, x], {n, 0, 10}]; Flatten[a]

CROSSREFS

Cf. A007283.

Sequence in context: A154570 A145961 A082928 * A247413 A108127 A207376

Adjacent sequences:  A139521 A139522 A139523 * A139525 A139526 A139527

KEYWORD

nonn,tabl

AUTHOR

Roger L. Bagula and Gary W. Adamson, Jun 09 2008

STATUS

approved

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Last modified September 19 15:21 EDT 2019. Contains 327198 sequences. (Running on oeis4.)