cp's OEIS Frontend

A147311 Riordan array [1, arcsin(tanh(x))].

%I A147311 #12 Jun 26 2018 04:53:57
%S A147311 1,0,1,0,0,1,0,-1,0,1,0,0,-4,0,1,0,5,0,-10,0,1,0,0,40,0,-20,0,1,0,-61,
%T A147311 0,175,0,-35,0,1,0,0,-768,0,560,0,-56,0,1,0,1385,0,-4996,0,1470,0,-84,
%U A147311 0,1,0,0,24320,0,-22720,0,3360,0,-120,0,1,0,-50521,0,214445,0,-81730,0,6930,0,-165,0,1
%N A147311 Riordan array [1, arcsin(tanh(x))].
%C A147311 Row sums are A012123. Inverse is A147312.
%C A147311 Production array is [cos(x),x] with a column of 0's prepended.
%C A147311 The product [sech(x),x]*A147311 is A147308.
%C A147311 Apart from signs, same as A147312. - _N. J. A. Sloane_, Nov 07 2008
%C A147311 Also the Bell transform of the Euler numbers. For the definition of the Bell transform see A264428. - _Peter Luschny_, Jan 29 2016
%e A147311 Triangle begins
%e A147311   1,
%e A147311   0,   1,
%e A147311   0,   0,   1,
%e A147311   0,  -1,   0,   1,
%e A147311   0,   0,  -4,   0,   1,
%e A147311   0,   5,   0, -10,   0,   1,
%e A147311   0,   0,  40,   0, -20,   0,   1
%p A147311 # The function BellMatrix is defined in A264428.
%p A147311 BellMatrix(n -> euler(n), 10); # _Peter Luschny_, Jan 29 2016
%t A147311 BellMatrix[f_, len_] := With[{t = Array[f, len, 0]}, Table[BellY[n, k, t], {n, 0, len - 1}, {k, 0, len - 1}]];
%t A147311 rows = 12;
%t A147311 B = BellMatrix[EulerE, rows];
%t A147311 Table[B[[n, k]], {n, 1, rows}, {k, 1, n}] // Flatten (* _Jean-François Alcover_, Jun 26 2018, after _Peter Luschny_ *)
%K A147311 easy,sign,tabl
%O A147311 0,13
%A A147311 _Paul Barry_, Nov 05 2008
%E A147311 More terms from _Jean-François Alcover_, Jun 26 2018