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 A157898 Triangle read by rows: inverse binomial transform of A059576 3

%I

%S 1,0,1,1,1,2,0,2,2,4,1,2,6,4,8,0,3,6,16,8,16,1,3,12,16,40,16,32,0,4,

%T 12,40,40,96,32,64,1,4,20,40,120,96,224,64,128,0,5,20,80,120,336,224,

%U 512,128,256

%N Triangle read by rows: inverse binomial transform of A059576

%C The inverse binomial transform of the triangle A059576 is given by multiplying the triangle with A130595 from the left.

%C Row sums are A097076(n+1) starting 1, 1, 4, 8, 21, 49, ...

%e First few rows of the triangle =

%e 1;

%e 0, 1;

%e 1, 1, 2;

%e 0, 2, 2, 4;

%e 1, 2, 6, 4, 8;

%e 0, 3, 6, 16, 8, 16;

%e 1, 3, 12, 16, 40, 16, 32;

%e 0, 4, 12, 40, 40, 96, 32, 64;

%e 1, 4, 20, 40, 120, 96, 224, 64, 128;

%e 0, 5, 20, 80, 120, 336, 224, 512, 128, 256;

%e ...

%p A059576 := proc (n, k)

%p if n = 0 then

%p return 1;

%p end if;

%p if k <= n and k >= 0 then

%p add((-1)^j*2^(n-j-1)*binomial(k, j)*binomial(n-j, k), j = 0 .. min(k, n-k))

%p else

%p 0 ;

%p end if

%p end proc:

%p A157898 := proc(n,k)

%p end proc: # _R. J. Mathar_, Feb 13 2013

%Y Cf. A059576, A097076

%K nonn,tabl,easy

%O 0,6

%A _Gary W. Adamson_ and _Roger L. Bagula_, Mar 08 2009

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Last modified May 8 13:26 EDT 2021. Contains 343666 sequences. (Running on oeis4.)