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A321907
If n > 1 is the k-th prime number, then a(n) = k!, otherwise a(n) = 0.
1
1, 1, 2, 0, 6, 0, 24, 0, 0, 0, 120, 0, 720, 0, 0, 0, 5040, 0, 40320, 0, 0, 0, 362880, 0, 0, 0, 0, 0, 3628800, 0, 39916800, 0, 0, 0, 0, 0, 479001600, 0, 0, 0, 6227020800, 0, 87178291200, 0, 0, 0, 1307674368000, 0, 0, 0, 0, 0, 20922789888000, 0, 0, 0, 0, 0
OFFSET
1,3
COMMENTS
1 is taken to be the zeroth prime number.
a(n) is the sum of coefficients of power sums symmetric functions in |y|! * s(y) / syt(y), where y is the integer partition with Heinz number n, s is Schur functions, and syt(y) is the number of standard Young tableaux of shape y.
MATHEMATICA
Table[If[n==1, 1, If[PrimeQ[n], PrimePi[n]!, 0]], {n, 40}]
PROG
(PARI) a(n) = if (n==1, 1, if (isprime(n), primepi(n)!, 0)); \\ Michel Marcus, Nov 23 2018
KEYWORD
nonn
AUTHOR
Gus Wiseman, Nov 21 2018
STATUS
approved