A111534 Main diagonal of table A111528.

1, 1, 4, 33, 416, 7045, 149472, 3804353, 112784896, 3812791581, 144643185600, 6081135558817, 280510445260800, 14080668974435141, 763890295406672896, 44529851124925034625, 2775373003913373810688, 184147301185264051623181

Offset: 0

Author

Paul D. Hanna, Aug 06 2005

Keywords

• nonn

Comments

For n>0, a(n) is divisible by n: a(n)/n = A111535(n).

Crossrefs

Cf: A111528 (table), A003319 (row 1), A111529 (row 2), A111530 (row 3), A111531 (row 4), A111532 (row 5), A111533 (row 6).

Programs

Mathematica

T[n_, k_] := T[n, k] = Which[n<0 || k<0, 0, k==0 || k==1, 1, n==0, k!, True, (T[n-1, k+1]-T[n-1, k])/n - Sum[T[n, j] T[n-1, k-j], {j, 1, k-1}]];
a[n_] := T[n, n];
Table[a[n], {n, 0, 17}] (* Jean-François Alcover, Aug 09 2018 *)

PARI

{a(n)=if(n<0,0,if(n==0,1, polcoeff(log(sum(m=0,n,(n-1+m)!/(n-1)!*x^m)),n)))}

Formula

a(n) = [x^n] Log( Sum_{m=0..n} (n-1+m)!/(n-1)!*x^m ).