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A101164 Triangle read by rows: Delannoy numbers minus binomial coefficients. 8


%S 0,0,0,0,1,0,0,2,2,0,0,3,7,3,0,0,4,15,15,4,0,0,5,26,43,26,5,0,0,6,40,

%T 94,94,40,6,0,0,7,57,175,251,175,57,7,0,0,8,77,293,555,555,293,77,8,0,

%U 0,9,100,455,1079,1431,1079,455,100,9,0,0,10,126,668,1911,3191,3191,1911

%N Triangle read by rows: Delannoy numbers minus binomial coefficients.

%C T(n,2) = A005449(n-2) for n>1;

%C T(n,3) = A101165(n-3) for n>2;

%C T(n,4) = A101166(n-4) for n>3;

%C sum of n-th row = A094706(n).

%H Reinhard Zumkeller, <a href="/A101164/b101164.txt">Rows n = 0..100 of table, flattened</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/DelannoyNumber.html">Delannoy Number</a>

%H Eric Weisstein's World of Mathematics, <a href="http://mathworld.wolfram.com/BinomialCoefficient.html">Binomial Coefficient</a>

%H <a href="/index/Pas#Pascal">Index entries for triangles and arrays related to Pascal's triangle</a>

%F T(n, k) = TD(n, k) - Binomial(n, k), 0<=k<=n, where Binomial=A007318 and TD defines the triangle of A008288.

%o (Haskell)

%o a101164 n k = a101164_tabl !! n !! k

%o a101164_row n = a101164_tabl !! n

%o a101164_tabl = zipWith (zipWith (-)) a008288_tabl a007318_tabl

%o -- _Reinhard Zumkeller_, Jul 30 2013

%Y Cf. A225413.

%K nonn,tabl

%O 0,8

%A _Reinhard Zumkeller_, Dec 03 2004

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Last modified February 19 20:51 EST 2019. Contains 320328 sequences. (Running on oeis4.)