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A371027 a(n) = Sum_{k=1..n} binomial(n, k) * Pochhammer(1/4, k) * 4^k * a(n - k) for n > 0 and a(0) = 1. Row sums of triangle A371026.

%I A371027 #7 Mar 08 2024 12:09:24
%S A371027 1,1,7,81,1299,26565,659655,19256265,645765435,24453391725,
%T A371027 1031685317775,47978413923825,2437962646702275,134374287343821525,
%U A371027 7984095179348863575,508687013361879977625,34593307096333435324875,2500919993138258679112125,191526329081848509391017375
%N A371027 a(n) = Sum_{k=1..n} binomial(n, k) * Pochhammer(1/4, k) * 4^k * a(n - k) for n > 0 and a(0) = 1. Row sums of triangle A371026.
%p A371027 a := proc(n) option remember; local k; if n = 0 then 1 else
%p A371027 add(binomial(n, k) * pochhammer(1/4, k) * 4^k * a(n - k), k = 1..n) fi end:
%p A371027 seq(a(n), n = 0..19);
%Y A371027 Cf. A371026, A007696.
%K A371027 nonn
%O A371027 0,3
%A A371027 _Peter Luschny_, Mar 08 2024