A111106 - OEIS

%I #18 Oct 19 2022 11:28:28

%S 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 10395,2190,441,100,25,6,1,0,135135,23535,3807,691,145,33,7,1,0,

%U 2027025,299880,40032,5880,1010,200,42,8,1

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

%C 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 T(n, k) = Sum_{j=0..n-k} T(n-1, k-1+j)*A111088(j).

%F Sum_{k=0..n} T(n, k) = A112934(n).

%F G.f.: 1/(1-xy/(1-x/(1-2x/(1-3x/(1-4x/(1-... (continued fraction). - _Paul Barry_, Jan 29 2009

%F Sum_{k=0..n} T(n,k)*2^(n-k) = A168441(n). - _Philippe Deléham_, Nov 28 2009

%e Rows begin:

%e   1;

%e   0,       1;

%e   0,       1,      1;

%e   0,       3,      2,     1;

%e   0,      15,      7,     3,    1;

%e   0,     105,     36,    12,    4,    1;

%e   0,     945,    249,    64,   18,    5,   1;

%e   0,   10395,   2190,   441,  100,   25,   6,  1:

%e   0,  135135,  23535,  3807,  691,  145,  33,  7, 1;

%e   0, 2027025, 299880, 40032, 5880, 1010, 200, 42, 8, 1;

%p # Uses function PMatrix from A357368.

%p PMatrix(10, n -> doublefactorial(2*n-3)); # _Peter Luschny_, Oct 19 2022

%Y Columns: A000007, A001147, A034430; diagonals: A000012, A001477, A055998.

%Y Cf. A084938, A111088, A112934, A168441.

%K easy,nonn,tabl

%O 0,8

%A _Philippe Deléham_, Oct 13 2005, Dec 20 2008