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

0,2

Links

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

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 *)

Prog

(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

Crossrefs

Cf. A127058, A127059.

Sequence in context: A121681 A135742 A144273 * A134147 A220066 A157303

Adjacent sequences: A127057 A127058 A127059 * A127061 A127062 A127063

Keyword

nonn

Author

Paul D. Hanna, Jan 04 2007

Extensions

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

Status

approved