A321907 If n > 1 is the k-th prime number, then a(n) = k!, otherwise a(n) = 0.

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.

Links

Table of n, a(n) for n=1..58.

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

Crossrefs

Row sums of A321900.

Cf. A000085, A049084, A056239, A082733, A124795, A153452, A296150, A296188, A296561, A300121, A304438, A317552, A317554, A321742-A321765, A321908.

Sequence in context: A126869 A094233 A094659 * A361522 A137437 A183189

Adjacent sequences: A321904 A321905 A321906 * A321908 A321909 A321910

Keyword

nonn

Author

Gus Wiseman, Nov 21 2018

Status

approved