A347041 Stirling transform of pi (A000720).

0, 0, 1, 5, 21, 88, 389, 1852, 9525, 52632, 310141, 1936489, 12749204, 88149847, 637769490, 4812457992, 37763509549, 307453610201, 2592851608305, 22626572045811, 204197274002794, 1905132039608335, 18370391387293756, 183001650861913887, 1882207129695280320

Offset

0,4

Links

Alois P. Heinz, Table of n, a(n) for n = 0..575

Formula

G.f.: Sum_{k>=0} pi(k)*x^k / Product_{j=1..k} (1-j*x).

E.g.f.: Sum_{k>=0} pi(k)*(exp(x)-1)^k/k!.

a(n) = Sum_{k=0..n} Stirling2(n,k)*pi(k).

Maple

b:= proc(n, m) option remember; `if`(n=0,
      numtheory[pi](m), m*b(n-1, m)+b(n-1, m+1))
    end:
a:= n-> b(n, 0):
seq(a(n), n=0..27);

Crossrefs

Cf. A000720, A008277, A048993, A230980, A307771.

Sequence in context: A010917 A277668 A270494 * A267268 A355117 A273643

Adjacent sequences: A347038 A347039 A347040 * A347042 A347043 A347044

Keyword

nonn

Author

Alois P. Heinz, Aug 13 2021

Status

approved