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a(n) = [x^n] x * Product_{j>=0} (1 + x^(2^j) + n*x^(2^(j+1))).
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%I #12 Mar 17 2021 19:59:44

%S 0,1,1,4,1,11,7,57,1,28,21,265,13,365,211,3616,1,69,55,1141,41,1828,

%T 1013,25439,25,1951,1405,41608,813,50519,27931,954305,1,166,137,5041,

%U 109,8363,4447,182638,81,10251,7183,327403,3961,372736,198997,9971521,49,9801

%N a(n) = [x^n] x * Product_{j>=0} (1 + x^(2^j) + n*x^(2^(j+1))).

%H Alois P. Heinz, <a href="/A342643/b342643.txt">Table of n, a(n) for n = 0..16384</a>

%F a(2^n) = 1 for n >= 0.

%p b:= proc(n, i) option remember; `if`(n<2, n, (h->

%p `if`(p=0, b(h, i), i*b(h, i)+b(h+1, i)))(iquo(n, 2, 'p')))

%p end:

%p a:= n-> b(n$2):

%p seq(a(n), n=0..55);

%Y Cf. A002487.

%K nonn,look

%O 0,4

%A _Alois P. Heinz_, Mar 17 2021