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A281853
Expansion of Sum_{k>=2} x^prime(k) / (1 - Sum_{k>=2} x^prime(k))^2.
0
0, 0, 1, 0, 1, 2, 1, 4, 3, 6, 10, 8, 19, 22, 26, 48, 53, 78, 112, 136, 205, 264, 354, 504, 639, 890, 1204, 1568, 2173, 2868, 3826, 5192, 6839, 9214, 12295, 16296, 21894, 28996, 38624, 51552, 68230, 90930, 120715, 159988, 212728, 281696, 373574, 495312, 655365, 868510, 1149161, 1520020, 2011591, 2658416, 3514446
OFFSET
1,6
COMMENTS
Total number of parts in all compositions (ordered partitions) of n into odd primes (A065091).
FORMULA
G.f.: Sum_{k>=2} x^prime(k) / (1 - Sum_{k>=2} x^prime(k))^2.
EXAMPLE
a(11) = 10 because we have [11], [5, 3, 3], [3, 5, 3], [3, 3, 5] and 1 + 3 + 3 + 3 = 10.
MATHEMATICA
nmax = 55; Rest[CoefficientList[Series[Sum[x^Prime[k], {k, 2, nmax}]/(1 - Sum[x^Prime[k], {k, 2, nmax}])^2, {x, 0, nmax}], x]]
CROSSREFS
KEYWORD
nonn
AUTHOR
Ilya Gutkovskiy, Jan 31 2017
STATUS
approved