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A128386 Expansion of c(3x^2)/(1-xc(3x^2)), c(x) the g.f. of A000108. 5
1, 1, 4, 7, 28, 58, 232, 523, 2092, 4966, 19864, 48838, 195352, 492724, 1970896, 5068915, 20275660, 52955950, 211823800, 560198962, 2240795848, 5987822380, 23951289520, 64563867454, 258255469816, 701383563388, 2805534253552 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is 3^C(n+1,2)=A047656(n+1). Series reversion of x(1+x)/(1+2x+4x^2).

LINKS

Table of n, a(n) for n=0..26.

A. Bostan, Computer Algebra for Lattice Path Combinatorics, Seminaire de Combinatoire Ph. Flajolet, March 28 2013.

FORMULA

G.f.: (sqrt(1-12x^2)+2x-1)/(2x(1-4x)); a(n)=(1/(n+1))sum{k=0..n+1, sum{j=0..k, C(n,k)C(k,j)C(2n-2k+j,n-2k+j)(-1)^(n-2k+j)2^j4^(k-j)}}; a(n)=sum{k=0..floor(n/2), C(n,n-k)*(n-2k+1)*3^k/(n-k+1)}; a(n)=sum{k=0..floor(n/2), A009766(n-k,k)*3^k};

a(n)=Sum_{k, 0<=k<=n}3^k*A120730(n,n-k) . - Philippe Deléham, Mar 03 2007

Conjecture: (n+1)*a(n) -4*(n+1)*a(n-1) +12*(2-n)*a(n-2)+ 48*(n-2)*a(n-3) = 0. - R. J. Mathar, Nov 14 2011

CROSSREFS

Sequence in context: A146085 A061668 A239025 * A149074 A149075 A149076

Adjacent sequences:  A128383 A128384 A128385 * A128387 A128388 A128389

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 28 2007

STATUS

approved

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Last modified October 21 13:05 EDT 2018. Contains 316422 sequences. (Running on oeis4.)