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A127628 G.f. 1/(1-6*x*c(x)) where c(x) is the g.f. of A000108. 6
1, 6, 42, 300, 2154, 15492, 111492, 802584, 5778090, 41600532, 299517996, 2156509416, 15526797252, 111792690600, 804906480840, 5795323452720, 41726317225770, 300429441596340, 2163091823919900, 15574260559056840 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Image of 6^n under the Catalan transform g(x)->g(xc(x)). The Hankel transform of this sequence and of the aerated version with g.f. 1/(1-6*x^2*c(x^2)) is 6^n. In general, the expansions of 1/(1-k*x*c(x)) and 1/(1-k*x^2*c(x^2)) have Hankel transform k^n.

LINKS

Table of n, a(n) for n=0..19.

FORMULA

a(n)=if(n=0,1,sum{k=1..n, C(2n-k-1,n-k)*k*6^k/n}); a(n)=sum{k=0..n, C(2n,n-k)(2k+1)5^k/(n+k+1)};

a(n) = Sum_{k, 0<=k<=n}A106566(n,k)*6^k . - Philippe Deléham, Feb 04 2007

a(n)= Sum{k, 0<=k<=n}A039599(n,k)*5^k. - Philippe Deléham, Sep 08 2007

a(0)=1, a(n)=(36*a(n-1)-6*A000108(n-1))/5 for n>=1 . - Philippe Deléham, Nov 27 2007

Conjecture: 5*n*a(n) +2*(15-28*n)*a(n-1) +72*(2*n-3)*a(n-2) =0. - R. J. Mathar, Nov 14 2011

CROSSREFS

Sequence in context: A055272 A155196 A147838 * A111602 A091164 A004982

Adjacent sequences:  A127625 A127626 A127627 * A127629 A127630 A127631

KEYWORD

nonn

AUTHOR

Paul Barry, Jan 20 2007

STATUS

approved

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Last modified February 21 14:36 EST 2018. Contains 299414 sequences. (Running on oeis4.)