A194122 - OEIS

%I #20 Mar 23 2019 20:05:26

%S 16,31,31,57,62,57,99,119,119,99,163,218,238,218,163,256,381,456,456,

%T 381,256,386,637,837,912,837,637,386,562,1023,1474,1749,1749,1474,

%U 1023,562,794,1585,2497,3223,3498,3223,2497,1585,794,1093,2379,4082

%N Triangular array: T(n,k) = C(n+4,k) + C(n+4,k+1) + C(n+4,k+2) + C(n+4,k+3) + C(n+4,k+4), 0 <= k <= n.

%H Muniru A Asiru, <a href="/A194122/b194122.txt">Rows n = 0..150 of triangle, flattened </a>

%e Triangle begins:

%e    16;

%e    31,  31;

%e    57,  62,  57;

%e    99, 119, 119,  99;

%e   163, 218, 238, 218, 163;

%p A194122 := proc(n,k) add(binomial(n+4,k+j),j=0..4) ; end proc: # _R. J. Mathar_, Aug 25 2011

%t T[n_, k_] := Sum[Binomial[n + 4, k + j], {j, 0, 4}]

%t Flatten[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]

%t (* as a sequence *)

%t TableForm[Table[T[n, k], {n, 0, 10}, {k, 0, n}]]

%t (* as an array *)

%o (GAP) Flat(List([0..9],n->List([0..n],k->Sum([0..4],j->Binomial(n+4,k+j))))); # _Muniru A Asiru_, Mar 17 2019

%Y Cf. A192915.

%K nonn,tabl

%O 0,1

%A _Clark Kimberling_, Aug 16 2011