A187002 - OEIS

%I #18 Nov 05 2025 15:22:20

%S 1,2,1,3,4,1,3,10,6,1,2,18,21,8,1,1,25,53,36,10,1,0,28,105,116,55,12,

%T 1,0,25,171,294,215,78,14,1,0,18,234,616,660,358,105,16,1,0,10,273,

%U 1098,1677,1287,553,136,18,1,0,4,273,1696,3640,3828,2275,808,171,20,1,0,1,234,2297,6890,9739,7735,3740,1131,210,22,1

%N Triangle T(n,m): column m is the expansion of (x+2*x^2+3*x^3+3*x^4+2*x^5+x^6)^m.

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

%F T(n,m) := sum(k=m..n, binomial(m,k-m) * sum(j=0..k, binomial(k,j) * binomial(j,n-3*k+2*j))).

%e 1,

%e 2,1,

%e 3,4,1,

%e 3,10,6,1,

%e 2,18,21,8,1,

%e 1,25,53,36,10,1,

%e 0,28,105,116,55,12,1,

%e 0,25,171,294,215,78,14,1

%o (Maxima) T(n,m) := sum(binomial(m,k-m) * sum(binomial(k,j) * binomial(j,n-3*k+2*j),j,0,k),k,m,n);

%K nonn,tabl

%O 1,2

%A _Vladimir Kruchinin_, Mar 01 2011