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%I #11 Mar 29 2022 07:42:25
%S 1,4,5,11,29,84,258,825,2717,9152,31382,109174,384370,1366936,4903140,
%T 17718165,64442205,235717800,866573070,3200179290,11865909990,
%U 44158628280,164881364700,617507304570,2319082988274,8731658843424,32953192276508,124635610132460
%N a(n) = [x^n] (3*x + 1)*(1 - sqrt(1 - 4*x))/(2*x).
%F D-finite with recurrence a(n) = a(n-1)*((14*n + 2)*(2*n - 3))/((7*n - 6)*(n + 1)) for n >= 2.
%F a(n) = A000108(n)+3*A000108(n-1). - _R. J. Mathar_, Mar 29 2022
%p alias(PS = ListTools:-PartialSums):
%p aList := proc(len) local a, k, P, T; a := 4; P := [1]; T := [1];
%p for k from 0 to len-1 do T := [op(T), a]; P := PS([op(P), a]); a := P[-1] od;
%p T end: aList(27);
%p # Alternative:
%p a := proc(n) option remember; if n = 0 then 1 elif n = 1 then 4 else
%p a(n-1)*((14*n + 2)*(2*n - 3))/((7*n - 6)*(n + 1)) fi end: seq(a(n), n = 0..27);
%Y a(n) = A352680(4, n).
%K nonn,easy
%O 0,2
%A _Peter Luschny_, Mar 27 2022
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