[Python] Sum up column values by special logic

Say we have an array like:

a = np.array([
[k11, k12, k13, k14, k15, k16, k17, k18],
[k21, k22, k23, k24, k25, k26, k27, k28],
[k31, k32, k33, k34, k35, k36, k37, k38],
[k41, k42, k43, k44, k45, k46, k47, k48]
])

const = C


I need to create a vector from this array like this (runge kutta 4):

result = np.array([
const * (k11 + 2*k21 + 2*k31 + k41),
const * (k12 + 2*k22 + 2*k32 + k42),
const * (k13 + 2*k23 + 2*k33 + k43),
....
const * (k18 + 2*k28 + 2*k38 + k48)
])


I am able to do this in cycle, but I am pretty sure numpy methods allow this in vectorised form.

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