A120022 a(n) = A120020(n)/n = coefficient of x^n in the n-th self-composition of the g.f. of A120010, divided by n, for n>=1.

1, 1, 3, 17, 142, 1558, 21155, 342584, 6448217, 138392304, 3336869488, 89325958048, 2629214627421, 84408934941424, 2935694381925743, 109967573757472768, 4414292541216287516, 189054708982869449056

Offset

1,3

Links

Table of n, a(n) for n=1..18.

Mathematica

a[n_] := Sum[((-1)^(j-i) n^(i-2) Binomial[2n-2j, n-j] Binomial[n+i-j, j-i] Binomial[n+i-j-1, i-1])/(n-j+1), {j, 1, n}, {i, 1, j}]; Array[a, 18] (* Jean-François Alcover, Nov 14 2016 *)

Prog

(PARI) a(n)=polcoeff((1-sqrt(1-4*x*(1-x)/(1-(n+1)*x*(1-x)+x*O(x^n))))/2, n)/n
(PARI) /* Alternate Formula: */ a(n)=sum(j=1, n, binomial(2*n-2*j, n-j)/(n-j+1)* sum(i=1, j, (-1)^(j-i)*binomial(n-j+i, j-i)*binomial(n-j+i-1, i-1)*n^(i-2)))

Crossrefs

Cf. A120010, A120019, A120020, A120021, A120016.

Sequence in context: A291842 A322137 A062873 * A001865 A189001 A087885

Adjacent sequences: A120019 A120020 A120021 * A120023 A120024 A120025

Keyword

nonn

Author

Paul D. Hanna, Jun 14 2006

Status

approved