A186333 - OEIS

%I #15 Feb 13 2023 07:57:40

%S 1,1,1,1,2,1,2,3,3,1,0,6,6,4,1,0,5,13,10,5,1,0,4,18,24,15,6,1,0,4,21,

%T 43,40,21,7,1,0,0,25,64,85,62,28,8,1,0,0,18,90,151,150,91,36,9,1,0,0,

%U 12,100,245,306,245,128,45,10,1,0,0,8,97,340,561,560,378,174,55,11,1

%N Triangle T(n,k), the coefficient of x^n in x^k*(1+x+x^2+2*x^3)^k, 1<=k<=n.

%C The Riordan array (1,x+x^2+x^3+2*x^4) without the column k=0.

%H Vladimir Kruchinin, <a href="http://arxiv.org/abs/1009.2565">Composition of ordinary generating functions</a>, arXiv:1009.2565 [math.CO], 2010.

%F T(n,k) = sum_{j=0..k} binomial(k,j) *sum_{i=0..n-k} binomial(j,i) *binomial(k-j,n-3*k+2*j-i) *2^(n-3*k+2*j-i), n>0, n>=k.

%e 1,

%e 1,1,

%e 1,2,1,

%e 2,3,3,1,

%e 0,6,6,4,1,

%e 0,5,13,10,5,1,

%e 0,4,18,24,15,6,1,

%e 0,4,21,43,40,21,7,1,

%e 0,0,25,64,85,62,28,8,1,

%e 0,0,18,90,151,150,91,36,9,1,

%e 0,0,12,100,245,306,245,128,45,10,1,

%e 0,0,8,97,340,561,560,378,174,55,11,1

%K nonn,tabl,easy

%O 1,5

%A _Vladimir Kruchinin_, Feb 17 2011