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%I A154948 #12 Sep 08 2022 08:45:40
%S A154948 1,1,1,2,3,1,2,6,5,1,3,10,14,7,1,3,15,30,26,9,1,4,21,55,70,42,11,1,4,
%T A154948 28,91,155,138,62,13,1,5,36,140,301,363,242,86,15,1,5,45,204,532,819,
%U A154948 743,390,114,17,1,6,55,285,876,1652,1925,1375,590,146,19,1
%N A154948 Riordan array ((1+x)/(1-x^2)^2, x(1+x)/(1-x)).
%C A154948 Row sums are A113300(n+1). Diagonal sums are A154949.
%C A154948 Product of A154950 and A007318.
%H A154948 G. C. Greubel, <a href="/A154948/b154948.txt">Rows n = 0..100 of triangle, flattened</a>
%F A154948 Number triangle T(n,k) = Sum_{j=0..n+1} C(n+1-j,k+1)*C(k-1,j).
%F A154948 T(n, k) = binomial(n+1,k+1)*2F1(-(n-k), -(k-1); -(n+1); -1). - _G. C. Greubel_, Feb 18 2020
%e A154948 Triangle begins
%e A154948   1;
%e A154948   1,  1;
%e A154948   2,  3,  1;
%e A154948   2,  6,  5,  1;
%e A154948   3, 10, 14,  7,  1;
%e A154948   3, 15, 30, 26,  9,  1;
%e A154948   4, 21, 55, 70, 42, 11, 1;
%p A154948 seq(seq( add(binomial(k-1, j)*binomial(n-j+1, k+1), j=0..n+1), k=0..n), n=0..10); # _G. C. Greubel_, Feb 18 2020
%t A154948 Table[Binomial[n+1, k+1]*Hypergeometric2F1[-n+k, -k+1, -n-1, -1], {n, 0, 5}, {k, 0, n}]//Flatten (* _G. C. Greubel_, Feb 18 2020 *)
%o A154948 (Magma) [ (&+[Binomial(k-1, j)*Binomial(n-j+1, k+1): j in [0..n+1]]): k in [0..n], n in [0..10]]; // _G. C. Greubel_, Feb 18 2020
%o A154948 (Sage) [[ sum(binomial(k-1, j)*binomial(n-j+1, k+1) for j in (0..n+1)) for k in (0..n)] for n in (0..10)] # _G. C. Greubel_, Feb 18 2020
%K A154948 easy,nonn,tabl
%O A154948 0,4
%A A154948 _Paul Barry_, Jan 17 2009
%E A154948 a(45)=0 removed by _Georg Fischer_, Feb 18 2020

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