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%I #6 Mar 30 2012 18:55:30
%S 1,1,2,3,7,14,35,86,235,660,1968,6078,19570,65129,224057,793794,
%T 2892656,10819274,41480851,162783153,653115031,2676107761,11187573667,
%U 47675621875,206936072980,914179405191,4107584622566,18759751255220,87036191538839,409986093418733
%N Diagonal sums of triangle A191490.
%H Vincenzo Librandi, <a href="/A191491/b191491.txt">Table of n, a(n) for n = 0..104</a>
%t f[n_, k_] := f[n, k] = f[n - 1, k] + (n - 1)f[n - 1, k - 1] + If[n == k, 1, 0]
%t f[_, 0] = 1;
%t f[0, _] = 0;
%t Table[Sum[f[n - k, k], {k, 0, n}], {n, 0, 100}]
%o (Maxima) P[0]:1$
%o P[n]:=(1+(n-1)*q)*P[n-1]+q^n$
%o makelist(sum(coeff(expand(P[n-k]),q^k),k,0,n),n,0,24);
%Y Cf. A191490.
%K nonn
%O 0,3
%A _Emanuele Munarini_, Jun 03 2011
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