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A135065 A127733 * A007318 as infinite lower triangular matrices. 1
1, 4, 4, 9, 18, 9, 16, 48, 48, 16, 25, 100, 150, 100, 25, 36, 180, 360, 360, 180, 36, 49, 294, 735, 980, 735, 294, 49, 64, 448, 1344, 2240, 2240, 1344, 448, 64, 81, 648, 2268, 4536, 5670, 4536, 2268, 648, 81, 100, 900, 3600, 8400, 12600, 12600, 8400, 3600 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

A135065 * [1/1, 1/2, 1/3,...] = A066524: (1, 6, 21, 60, 155,...).

Triangle T(n,k), 0<=k<=n, read by rows, given by (4,-7/4,17/28,-32/119,7/17,0,0,0,0,0,0,0,...) DELTA (4,-7/4,17/28,-32/119,7/17,0,0,0,0,0,0,0,...) where DELTA is the operator defined in A084938. - Philippe Deléham, Oct 27 2011

LINKS

G. C. Greubel, Table of n, a(n) for the first 50 rows

Mircea Merca, A Special Case of the Generalized Girard-Waring Formula J. Integer Sequences, Vol. 15 (2012), Article 12.5.7.

FORMULA

T(n,k) = binomial(n,k)*(n+1)^2 = A007318(n,k)*A000290(n+1). - Philippe Deléham, Oct 27 2011

T(n-1,k-1) = Sum_{i= -k..k} (-1)^i*(k^2-i^2)*binomial(n,k+i)*binomial(n,k-i). - Mircea Merca, Apr 05 2012

G.f.: (-1-x-x*y)/ (x+x*y-1)^3 . - R. J. Mathar, Aug 12 2015

EXAMPLE

First few rows of the triangle are:

1;

4, 4;

9, 18, 9;

16, 48, 48, 16;

25, 100, 150, 100, 25;

36, 180, 360, 360, 180, 36;

49, 294, 735, 980, 735, 294, 49.

MAPLE

with(combstruct):for n from 0 to 11 do seq(n*m*count(Combination(n), size=m), m = 1 .. n) od; - Zerinvary Lajos, Apr 09 2008

MATHEMATICA

Flatten[Table[Binomial[n, k](n+1)^2, {n, 0, 10}, {k, 0, n}]] (* Harvey P. Dale, Jul 12 2013 *)

CROSSREFS

Cf. A000290, A127733, A066524, A014477 (row sums), A084938.

Sequence in context: A203003 A319646 A214826 * A067553 A112683 A192030

Adjacent sequences:  A135062 A135063 A135064 * A135066 A135067 A135068

KEYWORD

nonn,tabl,easy

AUTHOR

Gary W. Adamson, Nov 16 2007

EXTENSIONS

Corrected by Zerinvary Lajos, Apr 09 2008

STATUS

approved

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Last modified November 19 05:29 EST 2018. Contains 317333 sequences. (Running on oeis4.)