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A111106 Riordan array (1, x*g(x)) where g(x) is g.f. of double factorials A001147.

%I A111106 #18 Oct 19 2022 11:28:28
%S A111106 1,0,1,0,1,1,0,3,2,1,0,15,7,3,1,0,105,36,12,4,1,0,945,249,64,18,5,1,0,
%T A111106 10395,2190,441,100,25,6,1,0,135135,23535,3807,691,145,33,7,1,0,
%U A111106 2027025,299880,40032,5880,1010,200,42,8,1
%N A111106 Riordan array (1, x*g(x)) where g(x) is g.f. of double factorials A001147.
%C A111106 Triangle T(n,k), 0 <= k <= n, given by [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, ...] DELTA [1, 0, 0, 0, 0, 0, 0, 0, 0, 0, ...] where DELTA is the operator defined in A084938.
%F A111106 T(n, k) = Sum_{j=0..n-k} T(n-1, k-1+j)*A111088(j).
%F A111106 Sum_{k=0..n} T(n, k) = A112934(n).
%F A111106 G.f.: 1/(1-xy/(1-x/(1-2x/(1-3x/(1-4x/(1-... (continued fraction). - _Paul Barry_, Jan 29 2009
%F A111106 Sum_{k=0..n} T(n,k)*2^(n-k) = A168441(n). - _Philippe Deléham_, Nov 28 2009
%e A111106 Rows begin:
%e A111106   1;
%e A111106   0,       1;
%e A111106   0,       1,      1;
%e A111106   0,       3,      2,     1;
%e A111106   0,      15,      7,     3,    1;
%e A111106   0,     105,     36,    12,    4,    1;
%e A111106   0,     945,    249,    64,   18,    5,   1;
%e A111106   0,   10395,   2190,   441,  100,   25,   6,  1:
%e A111106   0,  135135,  23535,  3807,  691,  145,  33,  7, 1;
%e A111106   0, 2027025, 299880, 40032, 5880, 1010, 200, 42, 8, 1;
%p A111106 # Uses function PMatrix from A357368.
%p A111106 PMatrix(10, n -> doublefactorial(2*n-3)); # _Peter Luschny_, Oct 19 2022
%Y A111106 Columns: A000007, A001147, A034430; diagonals: A000012, A001477, A055998.
%Y A111106 Cf. A084938, A111088, A112934, A168441.
%K A111106 easy,nonn,tabl
%O A111106 0,8
%A A111106 _Philippe Deléham_, Oct 13 2005, Dec 20 2008