A127060 Row sums of triangle A127058.

1, 4, 19, 132, 1253, 14808, 206503, 3298552, 59220265, 1179047100, 25767347387, 613141219356, 15780105110605, 436801028784112, 12941788708753999, 408718346076189360, 13707898517284016849, 486640514520848512692

Offset: 0

Author

Paul D. Hanna, Jan 04 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..400

Crossrefs

Cf. A127058, A127059.

Programs

Mathematica

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}]];
Table[Sum[T[n, j], {j,0,n}], {n,0,20}] (* G. C. Greubel, Jun 08 2019 *)

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];
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 */
lista(nn) = {my(T = tabl(nn)); vector(nn, k, vecsum(T[k, ]));}
lista(20) \\ Michel Marcus, Jun 09 2019

Sage

@CachedFunction
def T(n, k):
    if (k==n): return n+1
    else: return sum(T(j+k, k)*T(n-j, k+1) for j in (0..n-k-1))
def a(n): return sum(T(n,j) for j in (0..n))
[a(n) for n in (0..20)] # G. C. Greubel, Jun 08 2019

Extensions

a(17) corrected by G. C. Greubel, Jun 08 2019