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Table 1 Coefficients for p=2q+1

From: Bernoulli numbers, convolution sums and congruences of coefficients for certain generating functions

f ( p ) : =

a

b

c

d

∑ k = 1 p − 1 σ 1 ∗ ( 2 m k) σ 1 ∗ ( 2 n (p−k))

0

0

3â‹… 2 m + n + 1

− 2 m + n + 1

∑ k = 1 p − 1 σ 1 ∗ ( 2 m k) σ 3 ∗ ( 2 n (p−k))

5â‹… 2 m + 3 n + 1

− 2 m + 3 n + 2

5â‹… 2 m + 3 n

− 2 m + 3 n

∑ r + s + t = p σ 1 ∗ ( 2 m r) σ 1 ∗ ( 2 n s) σ 1 ∗ ( 2 l t)

5⋅ 2 m + n + l − 1

−3⋅ 2 m + n + l

2 m + n + l + 1

− 2 m + n + l − 1