Domb's numbers and Ramanujan–Sato type series for 1/π

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Conjectures involving arithmetical sequences (2012, background): “[4] contains some series for 1/π involving Domb numbers.”
Eisenstein series and Ramanujan-type series for 1/π (2010, background): “N.D. Baruah Department of Mathematical Sciences, Tezpur University, Napaam-784028, Sonitpur, Assam, India e-mail: nayan@tezu.ernet.in B.C. Berndt ( ) Department of Mathematics, University of Illinois, 1409 West Green St., Urbana, IL 61801, USA e-mail: berndt@illinois.edu 16 N.D. Baruah, B.C. Berndt ”
New analogues of Clausen’s identities arising from the theory of modular forms | NOVA. The University of Newcastle's Digital Repository (2011, methodology): “Most of these series can be derived using ideas presented in [9] and we stress again that their proofs are independent of the Clausen-type identities (1.”
New representations for Apéry-like sequences (2010, background): “the (alternating version of the) Domb numbers [7]”
Divergent Ramanujan-type supercongruences (2010, background): “The general machinery for proving Ramanujan-like series for 1/π [2, 4, 18] produces, in several cases, divergent instances like ∞ ∑”