OFFSET
1,2
LINKS
V. V. Kruchinin, Composition of ordinary generating functions, arXiv:1009.2565 [math.CO], 2010.
Vladimir Kruchinin, D. V. Kruchinin, Composita and their properties , arXiv:1103.2582 [math.CO], 2011-2013.
FORMULA
T(n,k) = Sum_{s=k..n} binomial(s,n-s) * Sum_{j=0..k} binomial(k,j) * binomial(j,s-3*k+2*j).
EXAMPLE
1,
2,1,
3,4,1,
4,10,6,1,
3,20,21,8,1,
1,31,56,36,10,1,
0,38,120,120,55,12,1,
0,38,213,322,220,78,14,1,
0,30,321,724,705,364,105,16,1
MAPLE
A186686 := proc(n, k) x*(1+2*x+3*x^2+4*x^3+3*x^4+x^5) ; expand(%^k) ; coeftayl(%, x=0, n) ; end proc: # R. J. Mathar, Mar 04 2011
MATHEMATICA
T[n_, k_] := Sum[Binomial[s, n-s]*Sum[Binomial[k, j]*Binomial[j, s - 3*k + 2*j], {j, 0, k}], {s, k, n}];
Table[T[n, k], {n, 1, 12}, {k, 1, n}] // Flatten (* Jean-François Alcover, Nov 29 2017 *)
CROSSREFS
KEYWORD
AUTHOR
Vladimir Kruchinin, Feb 28 2011
STATUS
approved