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A353156
a(0) = 1; a(n) = -Sum_{k=1..n} prime(k+1) * a(n-k).
0
1, -3, 4, -4, 2, 6, -22, 46, -74, 86, -40, -120, 450, -958, 1506, -1694, 744, 2500, -9184, 19422, -30450, 34032, -14178, -52286, 188038, -394724, 615102, -681110, 268666, 1089974, -3847390, 8021030, -12426638, 13632728, -5063588, -22711916, 78708912, -162966020, 251005706
OFFSET
0,2
FORMULA
G.f.: 1 / (1 + Sum_{k>=1} prime(k+1) * x^k).
MATHEMATICA
a[0] = 1; a[n_] := a[n] = -Sum[Prime[k + 1] a[n - k], {k, 1, n}]; Table[a[n], {n, 0, 38}]
nmax = 38; CoefficientList[Series[1/(1 + Sum[Prime[k + 1] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
KEYWORD
sign
AUTHOR
Ilya Gutkovskiy, Apr 27 2022
STATUS
approved