His goalscoring performances proved crucial to help Arenas reach the Copa del Rey final on two occasions (1917 and 1919).

[4] Barcelona were impressed enough to sign him still in 1919 and Sesúmaga didn't lose his goalscoring instinct in Catalonia, helping his new club reach the 1920 final and beat Athletic Bilbao 2–0.

He was a member of a legendary Barcelona team, coached by Jack Greenwell, that also included Paulino Alcántara, Sagibarba, Ricardo Zamora and Josep Samitier.

[2] On 28 August 1920, Sesúmaga went down in history as one of the eleven footballers who played in the first game of the Spain national team at the 1920 Summer Olympics, in an eventual 1–0 victory over Denmark.

[6] These goals made him the all-time top scorer of the Spain national team until he was overtaken two years later on 30 April 1922 by Paulino Alcántara.