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A127060 Row sums of triangle A127058. 3
1, 4, 19, 132, 1253, 14808, 206503, 3298552, 59220265, 1179047100, 25767347387, 613141219356, 15780105110605, 436801028784112, 12941788708753999, 408718346076189360, 13707898517284016849, 486640514520848512692 (list; graph; refs; listen; history; text; internal format)
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

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Last modified December 1 04:02 EST 2021. Contains 349426 sequences. (Running on oeis4.)