OFFSET
1,3
COMMENTS
EXAMPLE
1;
1, 3;
1, 15, 15, 1;
1, 43, 161, 105, 10;
1, 96, 855, 1680, 855, 96, 1;
1, 185, 3191, 13387, 17655, 7623, 945, 21;
1, 323, 9570, 72254, 188188, 188188, 72254, 9570, 323, 1;
1, 525, 24675, 302359, 1345605, 2499861, 2036125, 715725, 99414, 4410, 36;
1, 808, 56896, 1055320, 7329975, 22338816, 32152848, 22338816, 7329975, 1055320, 56896, 808, 1;
MAPLE
A001263 := proc(n, k) if n <=0 or k <=0 then 0 ; elif k > n then 0 ; else binomial(n-1, k-1)*binomial(n, k-1)/k ; end if; end proc:
A178657 := proc(n, k) (1-x)^(2*n-1)*add(A001263(n+2*l, 2*l+1)*x^l, l=0..20) ; expand(%) ; coeftayl(%, x=0, k) ; end proc: # R. J. Mathar, Aug 30 2011
MATHEMATICA
p[x_, n_] = (1 - x)^(2*n - 1)*Sum[(Binomial[2*k + n, 2*k] Binomial[ 2*k + n, 1 + 2*k]/(2*k + n))*x^k, {k, 0, Infinity}];
Table[CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x], {n, 2, 10}];
Flatten[%]
CROSSREFS
KEYWORD
nonn,tabf
AUTHOR
Roger L. Bagula, Jun 01 2010
STATUS
approved