OFFSET
1,4
LINKS
G. C. Greubel, Table of n, a(n) for n = 1..540
Peter Luschny, The Bell transform.
Retoz, Sous-dérangements, Mai 2021.
FORMULA
a(n) = Sum_{k=1..n} BM[n][k] where BM is the BellMatrix(j -> j mod n) as defined in A264428.
Assuming offset = 0:
a(n) = n! * [x^n] exp(1 + (x - 1)*exp(x)). - Contributed by C. L. Martin (Retoz), May 16 2021.
a(n) = Sum_{j=0..n} binomial(n, j) * (-2)^(n-j) * A005387(j). - G. C. Greubel, Nov 17 2022
MAPLE
# BellMatrix is defined in A264428.
a := proc(n) BellMatrix(j -> modp(j, n), n): add(i, i in %[n]) end:
seq(a(n), n=1..25);
# Or, assuming offset = 0:
ser := series(exp(1 + (x - 1)*exp(x)), x=0, 25):
seq(n!*coeff(ser, x, n), n = 0..24); # Contributed by C. L. Martin (Retoz), May 16 2021.
MATHEMATICA
With[{m=40}, CoefficientList[Series[Exp[(x-1)*Exp[x] +1], {x, 0, m}], x]*Range[0, m]!] (* G. C. Greubel, Nov 17 2022 *)
PROG
(Magma) R<x>:=PowerSeriesRing(Rationals(), 40); Coefficients(R!(Laplace( Exp((x-1)*Exp(x) + 1) ))); // G. C. Greubel, Nov 17 2022
(SageMath)
def A327006_list(prec):
P.<x> = PowerSeriesRing(QQ, prec)
return P( exp((x-1)*exp(x) +1) ).egf_to_ogf().list()
A327006_list(40) # G. C. Greubel, Nov 17 2022
CROSSREFS
KEYWORD
nonn
AUTHOR
Peter Luschny, Aug 13 2019
STATUS
approved