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A115197
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Convolution of generalized Catalan numbers A064062 (called C(n;2)).
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1
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1, 2, 7, 32, 169, 974, 5947, 37820, 247885, 1662890, 11362399, 78806936, 553386097, 3926523782, 28108587139, 202764451700, 1472446595221, 10755543924578, 78973277044903, 582558618222416, 4315238786662585
(list; graph; refs; listen; history; internal format)
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OFFSET
| 0,2
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COMMENTS
| Row sums of triangle A115193, called C(1,2).
The o.g.f. given below follows from the Riordan matrix structure of the triangle A115193. See the o.g.f. for the row polynomials of A115193.
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FORMULA
| a(n)= sum(A115193(n,m),m=0..n), n>=0.
G.f.: ((1+2*x*c(2*x))/(1+x))^2 = ((1-2*x) + 6*x*c(2*x))/(1+x)^2, with the o.g.f. c(x) of Catalan numbers A000108.
a(n)= sum(C(2;n-k)*C(2;k),k=0..n), n>=0, with C(2;n):= A064062(n).
a(n)=4*A178792(n)-3*(n+1)*A064062(n+1) [From Joseph Abate (abate2020(AT)webtv.net), Jun 21 2010]
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CROSSREFS
| Sequence in context: A183951 A108524 A006781 * A107593 A125277 A179488
Adjacent sequences: A115194 A115195 A115196 * A115198 A115199 A115200
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KEYWORD
| nonn
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AUTHOR
| Wolfdieter Lang (wolfdieter.lang(AT)physik.uni-karlsruhe.de), Feb 23 2006
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