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%I #11 Sep 10 2021 18:20:25
%S 1,1,4,13,37,130,427,1441,4954,16987,58843,204610,713893,2500183,
%T 8778478,30898309,108987427,385136680,1363252603,4832572951,
%U 17153677534,60961916965,216887253409,772400234074,2753261490919,9822393082513
%N Expansion of 1/sqrt(1-2x-5x^2-6x^3+9x^4).
%C In general, Sum_{k=0..n}, C(n-k,k)^2*a^k*b^(n-k) has expansion 1/sqrt(1-2bx-(2ab-b^2)x^2-2a*b^2*x^3+(ab)^2*x^4).
%H Michael De Vlieger, <a href="/A108489/b108489.txt">Table of n, a(n) for n = 0..1785</a>
%H Hacène Belbachir and Abdelghani Mehdaoui, <a href="https://doi.org/10.2989/16073606.2020.1729269">Recurrence relation associated with the sums of square binomial coefficients</a>, Quaestiones Mathematicae (2021) Vol. 44, Issue 5, 615-624.
%F a(n) = Sum_{k=0..n}, C(n-k, k)^2*3^k.
%F D-finite with recurrence: n*a(n) +(-2*n+1)*a(n-1) +5*(-n+1)*a(n-2) +3*(-2*n+3)*a(n-3) +9*(n-2)*a(n-4)=0. - _R. J. Mathar_, Feb 20 2015
%t Array[Sum[Binomial[# - k, k]^2*3^k, {k, 0, #}] &, 26, 0] (* _Michael De Vlieger_, Sep 10 2021 *)
%Y Cf. A108484.
%K easy,nonn
%O 0,3
%A _Paul Barry_, Jun 04 2005
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