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A128387 Expansion of c(5x^2)/(1-xc(5x^2)), where c(x) is the g.f. of A000108. 5
1, 1, 6, 11, 66, 146, 876, 2131, 12786, 32966, 197796, 530526, 3183156, 8786436, 52718616, 148733571, 892401426, 2561439806, 15368638836, 44731364266, 268388185596, 790211926076, 4741271556456, 14095578557486 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Hankel transform is 5^C(n+1,2). Reversion of x(1+x)/(1+2x+6x^2).

LINKS

Table of n, a(n) for n=0..23.

FORMULA

G.f.: (sqrt(1-20x^2)+2x-1)/(2x(1-6x)); 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^j*6^(k-j)}}; a(n)=sum{k=0..floor(n/2), C(n,n-k)*(n-2k+1)*5^k/(n-k+1)}; a(n)=sum{k=0..floor(n/2), A009766(n-k,k)*5^k};

a(n)=Sum_{k, 0<=k<=n}5^k*A120730(n,n-k) . - Philippe Deléham, Mar 03 2007

Conjecture: (n+1)*a(n) -6*(n+1)*a(n-1) +20*(2-n)*a(n-2) +120*(n-2)*a(n-3)=0. - R. J. Mathar, Nov 14 2011

CROSSREFS

Sequence in context: A073219 A110445 A305608 * A061519 A193664 A080875

Adjacent sequences:  A128384 A128385 A128386 * A128388 A128389 A128390

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 28 2007

STATUS

approved

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Last modified October 21 11:10 EDT 2018. Contains 316414 sequences. (Running on oeis4.)