OFFSET
0,3
LINKS
Alois P. Heinz, Table of n, a(n) for n = 0..150
FORMULA
a(n) = A261836(2n,n).
MAPLE
b:= proc(n, i, p, k) option remember;
`if`(i*(i+1)/2<n, 0, `if`(n=0, p!, b(n, i-1, p, k)+
`if`(i>n, 0, b(n-i, i-1, p+1, k)*binomial(i+k-1, k-1))))
end:
a:= n-> add(b(2*n$2, 0, n-i)*(-1)^i*binomial(n, i), i=0..n):
seq(a(n), n=0..20);
MATHEMATICA
b[n_, i_, p_, k_] := b[n, i, p, k] = If[i*(i+1)/2<n, 0, If[n==0, p!, b[n, i - 1, p, k] + If[i>n, 0, b[n-i, i-1, p+1, k]*Binomial[i+k-1, k-1]]]]; a[n_] := Sum[b[2*n, 2*n, 0, n-i]*(-1)^i*Binomial[n, i], {i, 0, n}]; Table[a[n], {n, 0, 20}] (* Jean-François Alcover, Feb 25 2017, translated from Maple *)
CROSSREFS
KEYWORD
nonn
AUTHOR
Alois P. Heinz, Sep 02 2015
STATUS
approved