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The paper 'Trisections, intersection forms and the Torelli group' by Peter Lambert-Cole quotes the following formula for the Casson invariant of a knot $K$ in a homology $3$-sphere in terms of the linking form $l$ on a Seifert surface $\Sigma$ for $K$ of genus $g$: $$ \lambda'(K)=\sum_{i=1}^g \big(l(a_i,a_i)l(b_i,b_i)-l(a_i,b_i)l(a_i,b_i)\big)+\sum_{1 \le i<j \le g} \big(l(a_i,a_j)l(b_i,b_j)-l(a_i,b_j)l(a_j,b_i)\big). $$ Here $\{a_i,b_i\}$ is a geometric symplectic basis for $\Sigma$.

Does anyone have a reference for this formula? I have looked for it in both Saveliev's and Akbulut & McCarthy's books, but I was not able to find anything similar.

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    $\begingroup$ Have you looked at Christine Lescop's book Global Surgery Formula for the Casson-Walker Invariant. (AM-140), Volume 140, Princeton University Press? $\endgroup$
    – Liviu Nicolaescu
    Commented Oct 11, 2021 at 11:21

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Maybe you've already found a source or this is irrelevant by now, but I believe I took it from Morita's paper "Casson's invariant for homology 3-spheres and characteristic classes of surface bundles I". Specifically Proposition 3.2.

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