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

0,3

Comments

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

Links

Table of n, a(n) for n=0..17.

Formula

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

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 *)

Prog

(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)))}

Crossrefs

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

Sequence in context: A343686 A364980 A360234 * A162655 A216135 A052885

Adjacent sequences: A111531 A111532 A111533 * A111535 A111536 A111537

Keyword

nonn

Author

Paul D. Hanna, Aug 06 2005

Status

approved