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A245552 G.f.: Sum_{n>=0} (2*n+1)*x^(n^2+n+1).

%I A245552 #19 Jul 24 2017 11:40:58
%S A245552 0,1,0,3,0,0,0,5,0,0,0,0,0,7,0,0,0,0,0,0,0,9,0,0,0,0,0,0,0,0,0,11,0,0,
%T A245552 0,0,0,0,0,0,0,0,0,13,0,0,0,0,0,0,0,0,0,0,0,0,0,15,0,0,0,0,0,0,0,0,0,
%U A245552 0,0,0,0,0,0,17,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,19
%N A245552 G.f.: Sum_{n>=0} (2*n+1)*x^(n^2+n+1).
%C A245552 Related to g.f. for A053187.
%C A245552 Apart from signs and a factor of 2, this is the classical Jacobi theta-function theta'_1(q), see A002483.
%H A245552 Antti Karttunen, <a href="/A245552/b245552.txt">Table of n, a(n) for n = 0..10101</a>
%F A245552 a(2*n+1) = A198954(n), a(2*n) = 0.- _Robert Israel_, Aug 05 2014
%t A245552 Join[{0},Flatten[Table[Join[{n,PadRight[{},n,0]}],{n,1,19,2}]]] (* _Harvey P. Dale_, Dec 14 2014 *)
%o A245552 (PARI)
%o A245552 A198954(n) = { my(m); if(issquare(8*n + 1, &m), m, 0) }; \\ This function from _Michael Somos_
%o A245552 A245552(n) = if(!(n%2),0,A198954((n-1)/2)); \\ After _Robert Israel_'s formula - _Antti Karttunen_, Jul 24 2017
%Y A245552 Cf. A002483, A053187, A198954.
%K A245552 nonn
%O A245552 0,4
%A A245552 _N. J. A. Sloane_, Aug 02 2014