A177808 - OEIS

%I #10 May 14 2019 22:06:44

%S 1,1,1,1,70,1,1,495,495,1,1,1820,12870,1820,1,1,4845,125970,125970,

%T 4845,1,1,10626,735471,2704156,735471,10626,1,1,20475,3108105,

%U 30421755,30421755,3108105,20475,1,1,35960,10518300,225792840,601080390,225792840,10518300,35960,1,1,58905,30260340,1251677700,7307872110,7307872110,1251677700,30260340,58905,1

%N Triangle T(n,m) = binomial(4*n, 4*m), 0 <= m <= n, read by rows.

%C Row sums are A070775(n).

%F Right-left symmetric: T(n,m) = T(n,n-m).

%e 1;

%e 1, 1;

%e 1, 70, 1;

%e 1, 495, 495, 1;

%e 1, 1820, 12870, 1820, 1;

%e 1, 4845, 125970, 125970, 4845, 1;

%e 1, 10626, 735471, 2704156, 735471, 10626, 1;

%e 1, 20475, 3108105, 30421755, 30421755, 3108105, 20475, 1;

%e 1, 35960, 10518300, 225792840, 601080390, 225792840, 10518300, 35960, 1;

%e 1, 58905, 30260340, 1251677700, 7307872110, 7307872110, 1251677700,30260340, 58905, 1;

%e 1, 91390, 76904685, 5586853480, 62852101650, 137846528820, 62852101650, 5586853480, 76904685, 91390, 1;

%p A177808 := proc(n,m) binomial(4*n,4*m) ; end proc: # _R. J. Mathar_, Dec 13 2010

%t t[n_, m_] = Binomial[n, 4*m];

%t Table[Table[t[n, m], {m, 0, Floor[n/4]}], {n, 0, 40, 4}];

%t Flatten[%]

%Y Cf. A086645, A034839, A070775.

%K nonn,tabl

%O 0,5

%A _Roger L. Bagula_, Dec 13 2010