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A177993 Triangle read by rows, A177990 * A007318.

%I A177993 #12 Apr 14 2021 05:23:44
%S A177993 1,1,1,2,3,1,2,4,3,1,3,8,9,5,1,3,9,13,11,5,1,4,15,28,31,20,7,1,4,16,
%T A177993 34,46,40,22,7,1,5,24,62,102,110,78,35,9,1,5,25,70,130,166,148,91,37,
%U A177993 9,1,6,35,115,250,376,400,301,157,54,11,1,6,36,125,295,496,610,553,367,174,56,11,1
%N A177993 Triangle read by rows, A177990 * A007318.
%H A177993 Andrew Howroyd, <a href="/A177993/b177993.txt">Table of n, a(n) for n = 0..1325</a> (rows 0..50)
%F A177993 As infinite lower triangular matrices, A177990 * Pascal's triangle, (A007318).
%F A177993 T(n,k) = binomial(n,k) + Sum_{j=0..floor(n/2)-1} binomial(2*j+1,k). - _Andrew Howroyd_, Apr 13 2021
%e A177993 First few rows of the triangle =
%e A177993 1;
%e A177993 1, 1;
%e A177993 2, 3, 1;
%e A177993 2, 4, 3, 1;
%e A177993 3, 8, 9, 5, 1;
%e A177993 3, 9, 13, 11, 5, 1;
%e A177993 4, 15, 28, 31, 20, 7, 1;
%e A177993 4, 16, 34, 46, 40, 22, 7, 1;
%e A177993 5, 24, 62, 102, 110, 78, 35, 9, 1;
%e A177993 5, 25, 70, 130, 166, 148, 91, 37, 9, 1;
%e A177993 6, 35, 115, 250, 376, 400, 301, 157, 54, 11, 1;
%e A177993 6, 36, 125, 295, 496, 610, 553, 367, 174, 56, 11, 1;
%e A177993 7, 48, 191, 515, 991, 1402, 1477, 1159, 669, 276, 77, 13, 1;
%e A177993 7, 49, 203, 581, 1211, 1897, 2269, 2083, 1461, 771, 297, 709, 13, 1;
%e A177993 ...
%o A177993 (PARI) T(n,k) = {binomial(n,k) + sum(j=0, n\2-1, binomial(2*j+1,k))} \\ _Andrew Howroyd_, Apr 13 2021
%Y A177993 Row sums are A061547(n+1).
%Y A177993 Cf. A177992 = A007318 * A177990.
%Y A177993 Cf. A061547.
%K A177993 nonn,tabl
%O A177993 0,4
%A A177993 _Gary W. Adamson_, May 16 2010
%E A177993 Terms a(55) and beyond from _Andrew Howroyd_, Apr 13 2021