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 A157100 Transform of Catalan numbers whose Hankel transform satisfies the Somos-4 recurrence. 1

%I

%S 1,2,3,6,14,37,105,312,956,2996,9554,30897,101083,333947,1112497,

%T 3732956,12605030,42800318,146046820,500555448,1722402304,5948047170,

%U 20607691518,71610355541,249520257107,871614139397,3051737703527

%N Transform of Catalan numbers whose Hankel transform satisfies the Somos-4 recurrence.

%C Hankel transform is A157101.

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

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

%F 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

%K easy,nonn

%O 0,2

%A _Paul Barry_, Feb 22 2009

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Last modified May 9 20:59 EDT 2021. Contains 343746 sequences. (Running on oeis4.)