A117852 Mirror image of A098473 formatted as a triangular array.

1, 2, 1, 6, 4, 1, 20, 18, 6, 1, 70, 80, 36, 8, 1, 252, 350, 200, 60, 10, 1, 924, 1512, 1050, 400, 90, 12, 1, 3432, 6468, 5292, 2450, 700, 126, 14, 1, 12870, 27456, 25872, 14112, 4900, 1120, 168, 16, 1, 48620, 115830, 123552, 77616, 31752, 8820, 1680, 216, 18, 1

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for the first 100 rows, flattened

Formula

Sum_{k=0..n} T(n,k)*x^k = A126869(n), A002426(n), A000984(n), A026375(n), A081671(n), A098409(n), A098410(n) for x = -2, -1, 0, 1, 2, 3, 4 respectively. - Philippe Deléham, Sep 28 2007

T(n,k) = binomial(n,k)*A000984(n-k). - Philippe Deléham, Dec 12 2009

O.g.f.: 1/sqrt( (1 - x*t)*(1 - (x + 4)*t) ) = 1 + (2 + x)*t + (6 + 4*x + x^2)*t^2 + .... - Peter Bala, Nov 10 2013

Example

Triangle begins:
    1;
    2,   1;
    6,   4,   1;
   20,  18,   6,   1;
   70,  80,  36,   8,   1;
  252, 350, 200,  60,  10,   1;
  ...

Maple

c:=n->binomial(2*n, n): T:=proc(n, k) if k<=n then binomial(n, k)*c(n-k) else 0 fi end: for n from 0 to 10 do seq(T(n, k), k=0..n) od; #

Mathematica

Table[ Binomial[n, k]*Binomial[2*n - 2*k, n - k], {n, 0, 10}, {k, 0, n} ] // Flatten (* G. C. Greubel, Mar 07 2017 *)

Crossrefs

Cf. A098473.

Sequence in context: A094527 A054335 A110681 * A080245 A080247 A078937

Adjacent sequences: A117849 A117850 A117851 * A117853 A117854 A117855

Keyword

nonn,tabl

Author

Farkas Janos Smile (smile_farkasjanos(AT)yahoo.com.au), Dec 21 2006

Extensions

Edited by N. J. A. Sloane at the suggestion of Andrew S. Plewe, Jun 12 2007

Status

approved