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A299168 Number of ordered ways of writing n-th prime number as a sum of n primes. 1
1, 0, 0, 0, 5, 6, 42, 64, 387, 5480, 10461, 113256, 507390, 1071084, 4882635, 44984560, 382362589, 891350154, 7469477771, 33066211100, 78673599501, 649785780710, 2884039365010, 22986956007816, 306912836483025, 1361558306986280, 3519406658042964 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,5

LINKS

Table of n, a(n) for n=1..27.

FORMULA

a(n) = [x^prime(n)] (Sum_{k>=1} x^prime(k))^n.

EXAMPLE

a(5) = 5 because fifth prime number is 11 and we have [3, 2, 2, 2, 2], [2, 3, 2, 2, 2], [2, 2, 3, 2, 2], [2, 2, 2, 3, 2] and [2, 2, 2, 2, 3].

MATHEMATICA

Table[SeriesCoefficient[Sum[x^Prime[k], {k, 1, n}]^n, {x, 0, Prime[n]}], {n, 1, 27}]

CROSSREFS

Cf. A000040, A000586, A000607, A023360, A056768, A070215, A073610, A098238, A117278, A121303, A219180, A224344, A259254, A265112.

Sequence in context: A047170 A137254 A262308 * A219516 A273050 A163481

Adjacent sequences:  A299165 A299166 A299167 * A299169 A299170 A299171

KEYWORD

nonn

AUTHOR

Ilya Gutkovskiy, Feb 04 2018

STATUS

approved

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Last modified August 22 00:43 EDT 2019. Contains 326169 sequences. (Running on oeis4.)