login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

Row sums of triangle A127058.
3

%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