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

Author

Gus Wiseman, Nov 21 2018

Keywords

• nonn

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.

Crossrefs

Row sums of A321900.

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

Programs

Mathematica

Table[If[n==1,1,If[PrimeQ[n],PrimePi[n]!,0]],{n,40}]

PARI

a(n) = if (n==1, 1, if (isprime(n), primepi(n)!, 0)); \\ Michel Marcus, Nov 23 2018