cp's OEIS Frontend

A201385 Irregular triangle T(n,k) (n >= 1, k >= 1) read by rows: T(n,1) = 2^n - 1; for k>1, T(n,k) = 0 for n <= 2*(k-1); otherwise T(n+1,k) = T(n,k-1) + T(n,k).

%I A201385 #38 Nov 08 2023 09:40:02
%S A201385 1,3,7,3,15,10,31,25,10,63,56,35,127,119,91,35,255,246,210,126,511,
%T A201385 501,456,336,126,1023,1012,957,792,462,2047,2035,1969,1749,1254,462,
%U A201385 4095,4082,4004,3718,3003,1716,8191,8177,8086,7722,6721,4719,1716
%N A201385 Irregular triangle T(n,k) (n >= 1, k >= 1) read by rows: T(n,1) = 2^n - 1; for k>1, T(n,k) = 0 for n <= 2*(k-1); otherwise T(n+1,k) = T(n,k-1) + T(n,k).
%C A201385 A "Pascal Staircase".
%C A201385 The zero entries simplify the definition, but are not part of the official triangle.
%H A201385 Alois P. Heinz, <a href="/A201385/b201385.txt">Rows n = 1..200, flattened</a>
%H A201385 Ozer Ozturk and Piotr Pragacz, <a href="http://arxiv.org/abs/1111.6612">On Schur function expansions of Thom polynomials</a>, arXiv:1111.6612 [math.AG], 2011-2012. See (59), p. 22.
%e A201385 Triangle begins:
%e A201385     1
%e A201385     3
%e A201385     7   3
%e A201385    15  10
%e A201385    31  25 10
%e A201385    63  56 35
%e A201385   127 119 91 35
%e A201385   ...
%t A201385 With[{rowmax=20},DeleteCases[Transpose[PadLeft[NestWhileList[Accumulate[#[[2;;-2]]]&,2^Range[rowmax]-1,Length[#]>2&]]],0,2]] (* _Paolo Xausa_, Nov 07 2023 *)
%Y A201385 Columns k = 1, 2, 3 give A000225, A000247, A272352(n+1).
%Y A201385 Row sums give A130783.
%K A201385 nonn,tabf,easy
%O A201385 1,2
%A A201385 _Jonathan Vos Post_, Nov 30 2011
%E A201385 Entry revised by _N. J. A. Sloane_, Nov 07 2023