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A127952 Triangle read by rows, T(n,k) = (n+1)*binomial(n-1,k-1).

%I A127952 #22 Feb 15 2022 07:34:38
%S A127952 1,0,2,0,3,3,0,4,8,4,0,5,15,15,5,0,6,24,36,24,6,0,7,35,70,70,35,7,0,8,
%T A127952 48,120,160,120,48,8,0,9,63,189,315,315,189,63,9,0,10,80,280,560,700,
%U A127952 560,280,80,10,0,11,99,396,924,1386,1386,924,396,99,11
%N A127952 Triangle read by rows, T(n,k) = (n+1)*binomial(n-1,k-1).
%C A127952 Row sums = A057711, starting (1, 2, 6, 16, 40, 96, ...).
%C A127952 T(2n,n) gives A033876(n-1) for n > 0. - _Alois P. Heinz_, Sep 04 2014
%H A127952 G. C. Greubel, <a href="/A127952/b127952.txt">Rows n=0..100 of triangle, flattened</a>
%e A127952 First few rows of the triangle:
%e A127952   1;
%e A127952   0, 2;
%e A127952   0, 3,  3;
%e A127952   0, 4,  8,  4;
%e A127952   0, 5, 15, 15,  5;
%e A127952   0, 6, 24, 36, 24,  6;
%e A127952   0, 7, 35, 70, 70, 35,  7;
%e A127952   ...
%p A127952 T := (n,k) -> (n+1)*binomial(n-1, k-1);
%p A127952 seq(print(seq(T(n,k),k= 0..n)),n=0..6); # _Peter Luschny_, Sep 02 2014
%t A127952 Table[(n+1)*Binomial[n-1, k-1], {n, 0, 10}, {k, 0, n}] // Flatten (* _G. C. Greubel_, May 05 2018 *)
%o A127952 (PARI) for(n=0,10, for(k=0,n, print1(if(n==0, 1,(n+1)*binomial(n-1,k-1)), ", "))) \\ _G. C. Greubel_, May 05 2018
%o A127952 (Magma) [[n le 0 select 1 else (n+1)*Binomial(n-1,k-1): k in [0..n]]: n in [0..10]]; // _G. C. Greubel_, May 05 2018
%Y A127952 Cf. A007318, A126615, A057711.
%K A127952 nonn,tabl
%O A127952 0,3
%A A127952 _Gary W. Adamson_, Feb 09 2007
%E A127952 Name corrected after a suggestion of _Joerg Arndt_ by _Peter Luschny_, Sep 02 2014