A156290 - OEIS

A156290

Triangle read by rows: alternating binomial coefficients with signs.

1, -4, 1, 15, -6, 1, -56, 28, -8, 1, 210, -120, 45, -10, 1, -792, 495, -220, 66, -12, 1, 3003, -2002, 1001, -364, 91, -14, 1, -11440, 8008, -4368, 1820, -560, 120, -16, 1, 43758, -31824, 18564, -8568, 3060, -816, 153, -18, 1, -167960, 125970, -77520

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OFFSET

1,2

COMMENTS

Alternating binomial coefficients in the closed form expression for sequence A156289.

The Example lines below show the connection with Pascal's triangle A007318.

REFERENCES

T. Myers and L. Shapiro, Some applications of the sequence 1, 5, 22, 93, 386, ... to Dyck paths and ordered trees, Congressus Numerant., 204 (2010), 93-104.

LINKS

Table of n, a(n) for n=1..48.

FORMULA

R(k,j)=(-1)^(k+j)*Binomial(2k,k+j), for 1<= j<=k, and 0 otherwise.

EXAMPLE

R(2,1)=-4, R(3,3)=1, R(4,2)=28.

Here is Pascal's triangle with the entries in the present triangle preceded by a *:

......................1

.....................1, 1

...................1, 2,*1

.................1, 3, 3, 1

................1, 4, 6,*4,*1