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Revision History for A110489

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A110489

Row sums of a triangle based on the Catalan numbers.
(history; published version)

#8 by Bruno Berselli at Tue Aug 29 04:52:24 EDT 2017

STATUS

proposed

approved

#7 by Michel Marcus at Tue Aug 29 02:46:21 EDT 2017

STATUS

editing

proposed

#6 by Michel Marcus at Tue Aug 29 02:46:14 EDT 2017

PROG

(PARI) a(n) = sum(k=0, n, sum(j=0, (n-k), 2*(j+1)*(k-1)^j*binomial(2*(n-k)+1, n-k-j)/ (n-k+j+2))); \\ Michel Marcus, Aug 29 2017

CROSSREFS

Cf. A110488.

STATUS

proposed

editing

#5 by G. C. Greubel at Tue Aug 29 02:29:27 EDT 2017

STATUS

editing

proposed

#4 by G. C. Greubel at Tue Aug 29 02:28:24 EDT 2017

LINKS

G. C. Greubel, <a href="/A110489/b110489.txt">Table of n, a(n) for n = 0..595</a>

FORMULA

a(n) =sum Sum_{k=0..n, sum} Sum_{j=0..(n-k, )} 2*(j+1)*(k-1)^j*C(2*(n-k)+1, n-k-j)*2*(j+1)/ (n-k+j+2)}}.

MATHEMATICA

T[n_, 0] := CatalanNumber[n]; T[n_, 1] := CatalanNumber[n]; T[n_, n_] := 1; T[n_, k_] := Sum[2*(j + 1)*(k - 1)^j*Binomial[2 (n - k) + 1, n - k - j]/(n - k + j + 2), {j, 0, n - k}]; Table[Sum[T[n, k], {k, 0, n}], {n, 0, 50}] (* G. C. Greubel, Aug 29 2017 *)

STATUS

approved

editing

#3 by Russ Cox at Fri Mar 30 18:59:09 EDT 2012

AUTHOR

_Paul Barry (pbarry(AT)wit.ie), _, Jul 22 2005

Discussion

Fri Mar 30

18:59

OEIS Server: https://oeis.org/edit/global/287

#2 by N. J. A. Sloane at Fri Feb 24 03:00:00 EST 2006

FORMULA

a(n)=sum{k=0..n, sum{j=0..n-k, (k-1)^j*C(2(n-k)+1, n-k-j)*2*(j+1)/(n-k+j+2)}}

KEYWORD

easy,nonn,new

#1 by N. J. A. Sloane at Wed Sep 21 03:00:00 EDT 2005

NAME

Row sums of a triangle based on the Catalan numbers.

DATA

1, 2, 5, 14, 43, 142, 497, 1828, 7037, 28326, 119361, 527748, 2454929, 12041410, 62354641, 340840118, 1963757863, 11896370734, 75549183725, 501393978466, 3467199478543, 24916100775758, 185646100106929, 1431332539961350

OFFSET

0,2

COMMENTS

Row sums of A110488.

FORMULA

a(n)=sum{k=0..n, sum{j=0..n-k,(k-1)^j*C(2(n-k)+1,n-k-j)*2*(j+1)/(n-k+j+2)}}

KEYWORD

easy,nonn

AUTHOR

Paul Barry (pbarry(AT)wit.ie), Jul 22 2005

STATUS

approved