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%I #13 Jun 18 2019 05:59:22
%S 1,4,19,132,1253,14808,206503,3298552,59220265,1179047100,25767347387,
%T 613141219356,15780105110605,436801028784112,12941788708753999,
%U 408718346076189360,13707898517284016849,486640514520848512692
%N Row sums of triangle A127058.
%H G. C. Greubel, <a href="/A127060/b127060.txt">Table of n, a(n) for n = 0..400</a>
%t T[n_, k_]:=T[n, k]=If[k==n, n+1, Sum[T[j+k,k]*T[n-j,k+1], {j,0,n-k-1}]];
%t Table[Sum[T[n, j], {j,0,n}], {n,0,20}] (* _G. C. Greubel_, Jun 08 2019 *)
%o (PARI) getT(n, k, T) = if (!T[n+1,k+1], T[n+1, k+1] = sum(j=0, n-k-1, getT(j+k, k, T)*getT(n-j, k+1, T))); T[n+1, k+1];
%o tabl(nn) = {my(T = matrix(nn+1, nn+1)); for (i=1, nn+1, T[i, i] = i); for (i=0, nn, for (j=0, i, T[i+1, j+1] = getT(i, j, T); ); ); T; } /* A127059 */
%o lista(nn) = {my(T = tabl(nn)); vector(nn, k, vecsum(T[k, ]));}
%o lista(20) \\ _Michel Marcus_, Jun 09 2019
%o (Sage)
%o @CachedFunction
%o def T(n, k):
%o if (k==n): return n+1
%o else: return sum(T(j+k, k)*T(n-j, k+1) for j in (0..n-k-1))
%o def a(n): return sum(T(n,j) for j in (0..n))
%o [a(n) for n in (0..20)] # _G. C. Greubel_, Jun 08 2019
%Y Cf. A127058, A127059.
%K nonn
%O 0,2
%A _Paul D. Hanna_, Jan 04 2007
%E a(17) corrected by _G. C. Greubel_, Jun 08 2019
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