cp's OEIS Frontend

A163946 Triangle read by rows, A033184 * A091768 (diagonalized as an infinite lower triangular matrix).

%I A163946 #16 Jan 22 2023 09:15:55
%S A163946 1,1,1,2,2,2,5,5,6,6,14,14,18,24,22,42,42,56,84,110,92,132,132,180,
%T A163946 288,440,552,426,429,429,594,990,1650,2484,2982,2150,1430,1430,2002,
%U A163946 3432,6050,10120,14910,17200,11708,4862,4862,6864,12012,22022,39468,65604,94600,105372,68282
%N A163946 Triangle read by rows, A033184 * A091768 (diagonalized as an infinite lower triangular matrix).
%C A163946 As an eigentriangle, equals A033184 * the diagonalized version of its eigensequence. (the eigensequence of triangle A033184 = A091768).
%C A163946 Right border = A091768, left border = Catalan sequence A000108.
%C A163946 Sum of n-th row terms = rightmost term of next row.
%F A163946 Triangle read by rows, A033184 * A091768 (diagonalized such that the right border = (1, 1, 2, 6, 22, 92, 426, 2150,...) i.e. A091768 prefaced with a 1; with the rest zeros).
%e A163946 First few rows of the triangle =
%e A163946   1;
%e A163946   1, 1;
%e A163946   2, 2, 2;
%e A163946   5, 5, 6, 6;
%e A163946   14, 14, 18, 24, 22;
%e A163946   42, 42, 56, 84, 110, 92;
%e A163946   132, 132, 180, 288, 440, 552, 426;
%e A163946   429, 429, 594, 990, 1650, 2484, 2982, 2150;
%e A163946   1430, 1430, 2002, 3432, 6050, 10120, 14910, 17200, 11708;
%e A163946   4862, 4862, 6864, 12012, 22022, 39468, 65604, 94600, 105372, 68282;
%e A163946   ...
%e A163946 Row 3 = (5, 5, 6, 6) = (5, 5, 3, 1) * (1, 1, 2, 6); where (5, 5, 3, 1) = row 3 of triangle A033184 and (1, 1, 2, 6) = the first 3 terms of A091768 prefaced with a 1.
%Y A163946 Cf. A033184, A091768, A000108, A071721.
%K A163946 nonn,tabl
%O A163946 0,4
%A A163946 _Gary W. Adamson_, Aug 06 2009