A307899 Expansion of 1/(1 + x * Sum_{k>=1} prime(k)*x^k).

1, 0, -2, -3, -1, 5, 10, 9, -4, -26, -43, -33, 35, 148, 219, 98, -316, -857, -983, 23, 2296, 4501, 3712, -2906, -14257, -21771, -10811, 28282, 81209, 97292, 7960, -207185, -431595, -386033, 219344, 1322141, 2134126, 1226554, -2443765, -7684081, -9726127, -1791806, 18712361, 41428590, 39753658

Offset: 0

Author

Ilya Gutkovskiy, May 04 2019

Keywords

• sign

Comments

Alternating antidiagonal sums of square array, in which row m equals the m-fold convolution of primes with themselves.

Crossrefs

Cf. A000040, A030017, A030018, A307898.

Programs

Mathematica

nmax = 44; CoefficientList[Series[1/(1 + x Sum[Prime[k] x^k, {k, 1, nmax}]), {x, 0, nmax}], x]
a[0] = 1; a[n_] := a[n] = -Sum[Prime[k] a[n - k - 1], {k, 1, n - 1}]; Table[a[n], {n, 0, 44}]

Formula

Recurrence: a(n+1) = -Sum_{k=1..n} prime(k)*a(n-k).