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A090317 Row sums of triangle in A090285. 3
1, 2, 7, 28, 118, 510, 2235, 9876, 43870, 195556, 873814, 3911168, 17527904, 78622982, 352911939, 1584927828, 7120769526, 32002212252, 143859840114, 646819996008, 2908670252676, 13081556909292, 58839348572574, 264674150692488, 1190649451348908, 5356483791828840, 24098774900561500 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Apply the inverse of the Riordan array (1/(1-x^2),x/(1+x)^2) to 2^n. - Paul Barry, Mar 13 2009

Hankel transform is A079935. - Paul Barry, Mar 13 2009

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

a(n+1) = A000108(n+1) + Sum_ {k=0..n} a(n-k)*A001700(k); a(0) = 1.

G.f.: (1-x^2*c(x)^4)/(1-2x*c(x)^2), where c(x) is the g.f. of the Catalan numbers A000108. - Paul Barry, Mar 13 2009

Recurrence: 2*(n+1)*(n+3)*a(n) = (17*n^2+56*n-21)*a(n-1) - 18*(n+4)*(2*n-3)*a(n-2). - Vaclav Kotesovec, Oct 14 2012

a(n) ~ 9^n/2^(n+2). - Vaclav Kotesovec, Oct 14 2012

MATHEMATICA

Table[SeriesCoefficient[(1-x^2*((1-Sqrt[1-4*x])/(2*x))^4)/(1-2*x*((1-Sqrt[1-4*x])/(2*x))^2), {x, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 14 2012 *)

PROG

(PARI) x='x+O('x^66); Vec((1-x^2*((1-sqrt(1-4*x))/(2*x))^4)/(1-2*x*((1-sqrt(1-4*x))/(2*x))^2)) \\ Joerg Arndt, May 11 2013

CROSSREFS

Cf. A000108 A001700 A090285.

Sequence in context: A150647 A150648 A150649 * A150650 A150651 A151298

Adjacent sequences:  A090314 A090315 A090316 * A090318 A090319 A090320

KEYWORD

easy,nonn

AUTHOR

Philippe Deléham, Jan 25 2004

EXTENSIONS

Term 15 corrected by Paul Barry, Mar 13 2009

STATUS

approved

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Last modified September 23 14:27 EDT 2014. Contains 247171 sequences.