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 A168577 Pascal's triangle, first two columns and diagonal removed. 0

%I #5 Mar 30 2012 17:34:35

%S 3,6,4,10,10,5,15,20,15,6,21,35,35,21,7,28,56,70,56,28,8,36,84,126,

%T 126,84,36,9,45,120,210,252,210,120,45,10,55,165,330,462,462,330,165,

%U 55,11,66,220,495,792,924,792,495,220,66,12,78,286,715,1287,1716,1716,1287

%N Pascal's triangle, first two columns and diagonal removed.

%C Row sums are 3, 10, 25, 56, 119, 246, .. (A000247).

%F T(n,k)= [x^k] ((x + 1)^n - x^n - n*x - 1), 2<=k<n.

%F T(n,k) = binomial(n,k).

%e 3;

%e 6, 4;

%e 10, 10, 5;

%e 15, 20, 15, 6;

%e 21, 35, 35, 21, 7;

%e 28, 56, 70, 56, 28, 8;

%e 36, 84, 126, 126, 84, 36, 9;

%e 45, 120, 210, 252, 210, 120, 45, 10;

%e 55, 165, 330, 462, 462, 330, 165, 55, 11;

%e 66, 220, 495, 792, 924, 792, 495, 220, 66, 12;

%e 78, 286, 715, 1287, 1716, 1716, 1287, 715, 286, 78, 13;

%t p[x_, n_] = ((x + 1)^n - x^n - n*x - 1)/x^2;

%t Table[CoefficientList[p[x, n], x], {n, 3, 13}];

%t Flatten[%]

%Y Cf. A007318, A104712

%K nonn,easy,tabl

%O 2,1

%A _Roger L. Bagula_, Nov 30 2009

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Last modified September 14 06:50 EDT 2024. Contains 375918 sequences. (Running on oeis4.)