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The coefficient problem is an essential topic in the theory of univalent functions theory. In the present paper, we consider a new subclass <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mi mathvariant="script">SQ</mi></semantics></math></inline-formula> of analytic functions with <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msup><mi>f</mi><mo>′</mo></msup><mrow><mo>(</mo><mi>z</mi><mo>)</mo></mrow></mrow></semantics></math></inline-formula> subordinated to <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mn>1</mn><mo>/</mo><msup><mrow><mo>(</mo><mn>1</mn><mo>−</mo><mi>z</mi><mo>)</mo></mrow><mn>2</mn></msup></mrow></semantics></math></inline-formula> in the open unit disk. This class was introduced and studied by Răducanu. Our main aim is to give the sharp upper bounds of the second Hankel determinant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">H</mi><mrow><mn>2</mn><mo>,</mo><mn>3</mn></mrow></msub><mfenced open="(" close=")"><mi>f</mi></mfenced></mrow></semantics></math></inline-formula> and the third Hankel determinant <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><msub><mi mathvariant="script">H</mi><mrow><mn>3</mn><mo>,</mo><mn>1</mn></mrow></msub><mfenced open="(" close=")"><mi>f</mi></mfenced></mrow></semantics></math></inline-formula> for <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>f</mi><mo>∈</mo><mi mathvariant="script">SQ</mi></mrow></semantics></math></inline-formula>. This may help to understand more properties of functions in this class and inspire further investigations on higher Hankel determinants for this or other popular sub-classes of univalent functions.