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A364842 Table read by antidiagonals: row n gives the Euler transform of the sequence (2,...,2,0,0,...) that contains n 2s followed by 0s.

%I A364842 #20 Nov 12 2023 13:32:37
%S A364842 1,1,2,1,2,3,1,2,5,4,1,2,5,8,5,1,2,5,10,14,6,1,2,5,10,18,20,7,1,2,5,
%T A364842 10,20,30,30,8,1,2,5,10,20,34,49,40,9,1,2,5,10,20,36,59,74,55,10,1,2,
%U A364842 5,10,20,36,63,94,110,70,11,1,2,5,10,20,36,65,104,149,158,91,12
%N A364842 Table read by antidiagonals: row n gives the Euler transform of the sequence (2,...,2,0,0,...) that contains n 2s followed by 0s.
%e A364842 Table begins:
%e A364842   | 0 1 2  3  4  5  6   7   8   9  10
%e A364842 --+----------------------------------
%e A364842 1 | 1 2 3  4  5  6  7   8   9  10  11
%e A364842 2 | 1 2 5  8 14 20 30  40  55  70  91
%e A364842 3 | 1 2 5 10 18 30 49  74 110 158 221
%e A364842 4 | 1 2 5 10 20 34 59  94 149 224 334
%e A364842 5 | 1 2 5 10 20 36 63 104 169 264 405
%e A364842 6 | 1 2 5 10 20 36 65 108 179 284 445
%e A364842 7 | 1 2 5 10 20 36 65 110 183 294 465
%e A364842 8 | 1 2 5 10 20 36 65 110 185 298 475
%e A364842 9 | 1 2 5 10 20 36 65 110 185 300 479
%t A364842 Seed[i_, n_] := ConstantArray[2, i]~Join~ConstantArray[0, n - i];
%t A364842 A364842Table[n_] := Table[Seed[i, n] // EulerTransform, {i, 1, n}]
%t A364842 (*EulerTransform is defined in A005195*)
%Y A364842 Cf. A000027 (row 1), A006918 (row 2), A117485 (row 3), A117486 ( row 4), A117487 (row 5), A160647 (row 6), A000712 (main diagonal).
%Y A364842 Analogous for initial 1s sequence A008284.
%Y A364842 Cf. A115994.
%K A364842 nonn,tabl
%O A364842 1,3
%A A364842 _Peter Kagey_, Nov 09 2023