A158687 - OEIS

%I #11 Apr 21 2015 04:47:30

%S 1,1,1,1,4,1,1,8,7,1,1,12,24,10,1,1,16,56,49,13,1,1,20,104,160,83,16,

%T 1,1,24,168,400,351,126,19,1,1,28,248,832,1120,656,178,22,1,1,32,344,

%U 1520,2912,2561,1102,239,25,1

%N Riordan array (1/(1-x),x(1+x)^2/(1-x)).

%C Row sums are A077936. Diagonal sums are A129847. Central terms are A059304.

%C Inverse of alternating signed version is A100326.

%F Number triangle T(n,k) = Sum_{j=0..n-k} C(n-j,k)*C(2k,j).

%F T(n,k) = T(n-1,k) + T(n-1,k-1) + 2*T(n-2,k-1) + T(n-3,k-1), T(0,0) = T(1,0) = T(1,1) = 1, T(n,k) = 0 if k<0 or if k>n. - _Philippe Deléham_, Nov 11 2013

%F G.f.: 1/(1-y-x*(1+y)^2). - _Vladimir Kruchinin_, Apr 21 2015

%e Number triangle begins

%e 1,

%e 1, 1,

%e 1, 4, 1,

%e 1, 8, 7, 1,

%e 1, 12, 24, 10, 1,

%e 1, 16, 56, 49, 13, 1,

%e 1, 20, 104, 160, 83, 16, 1

%Y Cf. A059304, A077936, A100326, A129847.

%K easy,nonn,tabl

%O 0,5

%A _Paul Barry_, Mar 24 2009