A127894 Inverse of Riordan array (1/(1-x)^3, x/(1-x)^3).

1, -3, 1, 12, -6, 1, -55, 33, -9, 1, 273, -182, 63, -12, 1, -1428, 1020, -408, 102, -15, 1, 7752, -5814, 2565, -760, 150, -18, 1, -43263, 33649, -15939, 5313, -1265, 207, -21, 1, 246675, -197340, 98670, -35880, 9750, -1950, 273, -24, 1

Offset

0,2

Comments

First column is (-1)^n*A001764(n+1). Row sums are (-1)^n*A006013(n). Inverse of A127893.

Links

G. C. Greubel, Rows n=0..100 of triangle, flattened

Example

Triangle begins
1,
-3, 1,
12, -6, 1,
-55, 33, -9, 1,
273, -182, 63, -12, 1,
-1428, 1020, -408, 102, -15, 1,
7752, -5814, 2565, -760, 150, -18, 1,
-43263, 33649, -15939, 5313, -1265, 207, -21, 1,
246675, -197340, 98670, -35880, 9750, -1950, 273, -24, 1,
-1430715, 1170585, -610740, 237510, -71253, 16443, -2842, 348, -27, 1,
8414640, -7012200, 3786588, -1553472, 503440, -129456, 26040, -3968, 432, -30, 1

Mathematica

Table[If[k == 0, (-1)^(n-1)*Binomial[3*n, n-k]/(2*n+1), (-1)^(n-k-1)*((k + 1)/(n))*Binomial[3*n, n-k-1]], {n, 1, 100}, {k, 0, n-1}] // Flatten (* G. C. Greubel, Apr 29 2018 *)

Prog

(PARI) for(n=1, 10, for(k=0, n-1, print1(if(k==0, (-1)^(n-1)*binomial(3*n, n-k)/(2*n+1), (-1)^(n-k-1)*((k+1)/n)*binomial(3*n, n-k-1)), ", "))) \\ G. C. Greubel, Apr 29 2018

Crossrefs

Cf. A001764, A006013, A127893.

Sequence in context: A113369 A249253 A201638 * A127898 A078938 A135888

Adjacent sequences: A127891 A127892 A127893 * A127895 A127896 A127897

Keyword

sign,tabl

Author

Paul Barry, Feb 04 2007

Extensions

Terms a(39) onward added by G. C. Greubel, Apr 29 2018

Status

approved