

A134058


Triangle read by rows, T(n,k) = 2*binomial(n,k) if k > 0, (0 <= k <= n), left column = (1,2,2,2,...).


7



1, 2, 2, 2, 4, 2, 2, 6, 6, 2, 2, 8, 12, 8, 2, 2, 10, 20, 20, 10, 2, 2, 12, 30, 40, 30, 12, 2, 2, 14, 42, 70, 70, 42, 14, 2, 2, 16, 56, 112, 140, 112, 56, 16, 2, 2, 18, 72, 168, 252, 252, 168, 72, 18, 2
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OFFSET

0,2


COMMENTS

Row sums = (1, 4, 8, 16, 32, 64, ...). A134059 = analogous triangle, replacing (1,2,2,2,...) with (1,3,3,3,...).
Triangle T(n,k), 0 <= k <= n, read by rows given by [2, 1, 0, 0, 0, 0, 0, ...] DELTA [2, 1, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.  Philippe Deléham, Oct 07 2007
Equals A028326 for all but the first term.  R. J. Mathar, Jun 08 2008
Warning: the row sums do not give A046055.  N. J. A. Sloane, Jul 08 2009


LINKS

Table of n, a(n) for n=0..54.


FORMULA

Double Pascal's triangle and replace leftmost column with (1,2,2,2,...).
M*A007318, where M = an infinite lower triangular matrix with (1,2,2,2,...) in the main diagonal and the rest zeros.
Sum_{k=0..n} T(n,k)= A151821(n+1).  Philippe Deléham, Sep 17 2009
G.f.: (1+x+y)/(1xy).  Vladimir Kruchinin, Apr 09 2015


EXAMPLE

First few rows of the triangle:
1
2, 2;
2, 4, 2;
2, 6, 6, 2;
2, 8, 12, 8, 2;
2, 10, 20, 20, 10, 2;
...


MATHEMATICA

T[n_, k_] := SeriesCoefficient[(1+x+y)/(1xy), {x, 0, nk}, {y, 0, k}]; Table[T[n, k], {n, 0, 9}, {k, 0, n}] // Flatten (* JeanFrançois Alcover, Apr 09 2015, after Vladimir Kruchinin *)


CROSSREFS

Cf. A134059.
Sequence in context: A292929 A049627 A278223 * A216955 A086973 A240131
Adjacent sequences: A134055 A134056 A134057 * A134059 A134060 A134061


KEYWORD

nonn,tabl


AUTHOR

Gary W. Adamson, Oct 05 2007


STATUS

approved



