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A307898
Expansion of 1/(1 - x * Sum_{k>=1} prime(k)*x^k).
2
1, 0, 2, 3, 9, 19, 48, 107, 258, 594, 1405, 3277, 7693, 18004, 42203, 98834, 231592, 542497, 1271003, 2977529, 6975674, 16342011, 38285178, 89691782, 210124363, 492265243, 1153247379, 2701752062, 6329489153, 14828313076, 34738805240, 81383803849, 190660665579, 446667359857, 1046423138962
OFFSET
0,3
COMMENTS
Antidiagonal sums of square array, in which row m equals the m-fold convolution of primes with themselves.
FORMULA
Recurrence: a(n+1) = Sum_{k=1..n} prime(k)*a(n-k).
MATHEMATICA
nmax = 34; 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, 34}]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, May 04 2019
STATUS
approved