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A157100 Transform of Catalan numbers whose Hankel transform satisfies the Somos-4 recurrence. 1
1, 2, 3, 6, 14, 37, 105, 312, 956, 2996, 9554, 30897, 101083, 333947, 1112497, 3732956, 12605030, 42800318, 146046820, 500555448, 1722402304, 5948047170, 20607691518, 71610355541, 249520257107, 871614139397, 3051737703527 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Hankel transform is A157101.

LINKS

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

FORMULA

G.f.: (1+x)*c(x(1-x^2)), c(x) the g.f. of A000108;

a(n)=sum{k=0..n, (-1)^C(n-k,2)*C(k,floor((n-k)/2))*A000108(k)}.

Conjecture: (n+1)*a(n) +(-5*n+1)*a(n-1) +2*(2*n-1)*a(n-2) +2*(2*n-7)*a(n-3) +2*(-2*n+7)*a(n-4)=0. - R. J. Mathar, Feb 05 2015

CROSSREFS

Sequence in context: A275774 A001420 A049339 * A081293 A193215 A007611

Adjacent sequences:  A157097 A157098 A157099 * A157101 A157102 A157103

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Feb 22 2009

STATUS

approved

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Last modified December 14 21:33 EST 2017. Contains 296020 sequences.