# Greetings from The On-Line Encyclopedia of Integer Sequences! http://oeis.org/

Search: id:a133138
Showing 1-1 of 1

%I A133138 #21 May 19 2018 02:29:27
%S A133138 2,2,2,1,3,2,1,3,4,2,1,4,6,5,2,1,5,10,10,6,2,1,6,15,20,15,7,2,1,7,21,
%T A133138 35,35,21,8,2,1,8,28,56,70,56,28,9,2,1,9,36,84,126,126,84,36,10,2,1,
%U A133138 10,45,120,210,252,210,120,45,11,2
%N A133138 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.
%F A133138 From _R. J. Mathar_, Jun 12 2008: (Start)
%F A133138 T(n,k) = A007318(n,k), 0 <= k < n-1.
%F A133138 T(n,k) = A007318(n,k)+1, n-1 <= k <= n.
%F A133138 Sum_{k=0..n} T(n,k) = A133140(n). (End)
%F A133138 T(n,k) = A007318(n,k) + A097806(n,k). - _Franck Maminirina Ramaharo_, May 18 2018
%e A133138 Triangle T(n,k) begins:
%e A133138 n/k 0   1   2    3    4    5    6    7    8    9  10  11  12
%e A133138 0:  2
%e A133138 1:  2   2
%e A133138 2:  1   3   2
%e A133138 3:  1   3   4    2
%e A133138 4:  1   4   6    5    2
%e A133138 5:  1   5  10   10    6    2
%e A133138 6:  1   6  15   20   15    7    2
%e A133138 7:  1   7  21   35   35   21    8    2
%e A133138 8:  1   8  28   56   70   56   28    9    2
%e A133138 9:  1   9  36   84  126  126   84   36   10    2
%e A133138 10: 1  10  45  120  210  252  210  120   45   11   2
%e A133138 11: 1  11  55  165  330  462  462  330  165   55  12   2
%e A133138 12: 1  12  66  220  495  792  924  792  495  220  66  13   2
%e A133138 ... - _Franck Maminirina Ramaharo_, May 18 2018
%t A133138 q[n_] := (1+x)*((1+x)^(n-1) + x^(n-1)); t[n_, k_] := Coefficient[q[n], x, k]; Table[t[n, k], {n, 0, 10}, {k, 0, n}] // Flatten (* _Jean-François Alcover_, Dec 16 2013 *)
%o A133138 (Maxima)
%o A133138 Q(n, x) := (1 + x)*((1 + x)^(n - 1) + x^(n - 1))$
%o A133138 t(n,k) := ratcoef(expand(Q(n, x)), x, k)$
%o A133138 for n:0 thru 20 do print(makelist(t(n, k), k, 0, n)); /* _Franck Maminirina Ramaharo_, May 18 2018 */
%Y A133138 Cf. A133135.
%K A133138 nonn,tabl
%O A133138 0,1
%A A133138 _Paul Curtz_, Sep 21 2007
%E A133138 Edited by _R. J. Mathar_, Jun 12 2008

# Content is available under The OEIS End-User License Agreement: http://oeis.org/LICENSE