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
Keywords
Crossrefs
Programs
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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 ).
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