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Triangle T(n,k) of the coefficients of the polynomials Q(n,x)=(1+x)[(1+x)^(n-1)+x^(n-1)], Q(0,x)=2, in front of x^k.

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T(n,k)=A007318(n,k), 0<=k<n-1. T(n,k)=A007318(n,k)+1, n-1<=k<=n. Sum(k=0..n) T(n,k) = A133140(n). - R. J. Mathar, Jun 12 2008

From R. J. Mathar, Jun 12 2008: (Start)

T(n,k) = A007318(n,k), 0 <= k < n-1.

T(n,k) = A007318(n,k)+1, n-1 <= k <= n.

Sum_{k=0..n} T(n,k) = A133140(n). (End)

... - Franck Maminirina Ramaharo, May 18 2018

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n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 13

5: 1 5 10 10 6 2

6: 1 6 15 20 15 7 2

7: 1 7 21 35 35 21 8 2

8: 1 8 28 56 70 56 28 9 2

9: 1 9 36 84 126 126 84 36 10 2

10: 1 10 45 120 210 252 210 120 45 11 2

11: 1 11 55 165 330 462 462 330 165 55 12 2

12: 1 12 66 220 495 792 924 792 495 220 66 13 2

13: 1 13 78 286 715 1287 1716 1716 1287 715 286 78 14 2

n/k 0 1 2 3 4 5 6 7 8 9 10 11 12 13 14

4: 1 4 6 5 2

5: 1 5 10 10 6 2

6: 1 6 15 20 15 7 2

7: 1 7 21 35 35 21 8 2

8: 1 8 28 56 70 56 28 9 2

9: 1 9 36 84 126 126 84 36 10 2

10: 1 10 45 120 210 252 210 120 45 11 2

11: 1 11 55 165 330 462 462 330 165 55 12 2

12: 1 12 66 220 495 792 924 792 495 220 66 13 2

13: 1 13 78 286 715 1287 1716 1716 1287 715 286 78 14 2

14: 1 14 91 364 1001 2002 3003 3432 3003 2002 1001 364 91 15 2

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