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 A156290 Triangle read by rows: alternating binomial coefficients with signs. 1
 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 (list; table; graph; refs; listen; history; text; internal format)
 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 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 ..............1, 5, 10, 10, 5, 1 ............1, 6, 15, 20,*15,*6,*1 ..........1, 7, 21, 35, 35, 21, 7, 1 ........1, 8, 28, 56, 70,*56,*28,*8,*1 ... MATHEMATICA R[m_] := Flatten[Table[(-1)^(k + j) Binomial[2 k, k + j], {k, 1, m}, {j, 1, k}]] CROSSREFS Coefficient factor in elements of sequence A156289, the inverse of lower triangular matrix A156308. Cf. A007318. Sequence in context: A229468 A319039 A107873 * A080419 A095307 A159764 Adjacent sequences:  A156287 A156288 A156289 * A156291 A156292 A156293 KEYWORD easy,sign,tabl AUTHOR Hartmut F. W. Hoft, Feb 07 2009 EXTENSIONS Edited by N. J. A. Sloane, Apr 05 2011 STATUS approved

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Last modified June 20 01:36 EDT 2019. Contains 324223 sequences. (Running on oeis4.)