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A134309 Triangle read by rows, where row n consists of n zeros followed by 2^(n-1). 14
1, 0, 1, 0, 0, 2, 0, 0, 0, 4, 0, 0, 0, 0, 8, 0, 0, 0, 0, 0, 16, 0, 0, 0, 0, 0, 0, 32, 0, 0, 0, 0, 0, 0, 0, 64, 0, 0, 0, 0, 0, 0, 0, 0, 128, 0, 0, 0, 0, 0, 0, 0, 0, 0, 256, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 512, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1024, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 2048, 0, 0, 0, 0, 0, 0, 0 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,6

COMMENTS

As infinite lower triangular matrices, binomial transform of A134309 = A082137. A134309 * A007318 = A055372. A134309 * [1,2,3,...] = A057711: (1, 2, 6, 16, 40, 96, 224,...).

Triangle read by rows given by [0,0,0,0,0,0,0,0,...] DELTA [1,1,0,0,0,0,0,0,0,...] where DELTA is the operator defined in A084938 . - Philippe Deléham, Oct 20 2007

LINKS

Table of n, a(n) for n=0..97.

FORMULA

Triangle, T(0,0) = 1, then for n>0, n zeros followed by 2^(n-1). Infinite lower triangular matrix with (1, 1, 2, 4, 8, 16,...) in the main diagonal and the rest zeros.

G.f.: (1-y*x)/(1-2*y*x). Philippe Deléham, Feb 04 2012

Sum_{k, 0<=k<=n} T(n,k)*x^k = A000007(n), A011782(n), A081294(n), A081341(n), A092811(n), A093143(n), A067419(n) for x = 0, 1, 2, 3, 4, 5, 6 respectively . - Philippe Deléham, Feb 04 2012

EXAMPLE

First few rows of the triangle are:

1;

0, 1;

0, 0, 2;

0, 0, 0, 4;

0, 0, 0, 0, 8;

...

CROSSREFS

Cf. A082137, A055372, A057711.

Sequence in context: A245527 A287871 A135416 * A051516 A236799 A208274

Adjacent sequences:  A134306 A134307 A134308 * A134310 A134311 A134312

KEYWORD

nonn,tabl

AUTHOR

Gary W. Adamson, Oct 19 2007

STATUS

approved

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Last modified February 20 00:28 EST 2019. Contains 320329 sequences. (Running on oeis4.)