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A075779 Triangle T(n,k) = f(n,k,n-1), n >= 2, 1 <= k <= n-1, where f is given below. 4
2, 6, 6, 12, 16, 12, 20, 35, 35, 20, 30, 66, 84, 66, 30, 42, 112, 175, 175, 112, 42, 56, 176, 328, 400, 328, 176, 56, 72, 261, 567, 819, 819, 567, 261, 72, 90, 370, 920, 1540, 1820, 1540, 920, 370, 90, 110, 506, 1419, 2706, 3696, 3696, 2706, 1419, 506, 110, 132, 672 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

2,1

COMMENTS

Row sums give sequence A033484(n)*(n+2). Essentially same triangle as A051597(n,k)*(n+2). - Philippe Deléham, Oct 01 2003

LINKS

Table of n, a(n) for n=2..58.

Michel Lassalle, A new family of positive integers

FORMULA

f(n, p, k) = binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1).

EXAMPLE

2; 6,6; 12,16,12; 20,35,35,20; ...

MAPLE

f := proc(n, p, k) convert( binomial(n, k)*hypergeom([1-k, -p, p-n], [1-n, 1], 1), `StandardFunctions`); end;

MATHEMATICA

t[n_, k_] := n*HypergeometricPFQ[{-k, 2-n, k-n}, {1, 1-n}, 1]; Table[t[n, k], {n, 2, 12}, {k, 1, n-1}] // Flatten (* Jean-François Alcover, Jan 14 2014 *)

CROSSREFS

Cf. A014410 and A007318 for f(n, k, n), A075779 and A075798 for f(n, k, n-1) and A075780 and A075837 for f(n, k, n-2).

Cf. A033484 A051597.

Sequence in context: A064797 A053319 A253215 * A241301 A140880 A065420

Adjacent sequences:  A075776 A075777 A075778 * A075780 A075781 A075782

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 17 2002

STATUS

approved

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Last modified April 17 19:37 EDT 2021. Contains 343070 sequences. (Running on oeis4.)