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A075798 Triangle T(n,k) = f(n,k,n-1), n >= 0, 0 <= k <= n, where f is given below. 4
1, 1, 1, 1, 2, 1, 1, 6, 6, 1, 1, 12, 16, 12, 1, 1, 20, 35, 35, 20, 1, 1, 30, 66, 84, 66, 30, 1, 1, 42, 112, 175, 175, 112, 42, 1, 1, 56, 176, 328, 400, 328, 176, 56, 1, 1, 72, 261, 567, 819, 819, 567, 261, 72, 1, 1, 90, 370, 920, 1540, 1820, 1540, 920, 370, 90, 1, 1, 110, 506, 1419, 2706, 3696, 3696, 2706, 1419, 506, 110, 1, 1, 132, 672 (list; table; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..81.

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

1; 1,1; 1,2,1; 1,6,6,1; ...

MAPLE

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

MATHEMATICA

f[n_, p_, k_] := Binomial[n, k]*HypergeometricPFQ[{1 - k, -p, p-n}, {1-n, 1}, 1]; t[n_, n_] = t[_, 0] = 1; t[n_, k_] := f[n, k, n-1]; Table[t[n, k], {n, 0, 12}, {k, 0, n}] // Flatten (* Jean-Fran├žois Alcover, Jan 17 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).

Sequence in context: A255914 A143185 A157635 * A155864 A145903 A223257

Adjacent sequences:  A075795 A075796 A075797 * A075799 A075800 A075801

KEYWORD

nonn,tabl

AUTHOR

N. J. A. Sloane, Oct 17 2002

STATUS

approved

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Last modified September 24 07:01 EDT 2020. Contains 337317 sequences. (Running on oeis4.)