A182666 E.g.f.: Product_{n>=1} Sum_{k>=0} (x^k/k!)^n.

1, 1, 3, 13, 67, 471, 3591, 33573, 329043, 3919387, 47827093, 663429603, 9764977399, 156308277139, 2653548775671, 48880554540093, 934560430625523, 19120475459863299, 413057291727064689, 9325822483756554831, 221409989926026560757, 5513060361601128645777

Offset

0,3

Links

Alois P. Heinz, Table of n, a(n) for n = 0..444 (first 301 terms from Vaclav Kotesovec)

Kévin Perrot, Sylvain Sené, and Léah Tapin, On countings and enumerations of block-parallel automata networks, arXiv:2304.09664 [cs.DM], 2023.

Example

E.g.f.: A(x) = 1 + x + 3*x^2/2! + 13*x^3/3! + 67*x^4/4! + 471*x^5/5! + 3591*x^6/6! +...
where
A(x) = [Sum_{k>=0} x^k/k!] * [Sum_{k>=0} (x^k/k!)^2] * [Sum_{k>=0} (x^k/k!)^3] * [Sum_{k>=0} (x^k/k!)^4] *...

Maple

b:= proc(n, i) option remember; `if`(n=0, 1, `if`(i<1, 0, add(
      b(n-i*j, i-1)*combinat[multinomial](n, n-i*j, j$i), j=0..n/i)))
    end:
a:= n-> b(n$2):
seq(a(n), n=0..23);  # Alois P. Heinz, Jul 18 2023

Mathematica

multinomial[n_, k_List] := n!/Times @@ (k!);
b[n_, i_] := b[n, i] = If[n == 0, 1, If[i < 1, 0, Sum[b[n - i*j, i - 1]* multinomial[n, Join[{n - i*j}, Table[j, {i}]]], {j, 0, n/i}]]];
a[n_] := b[n, n];
Table[a[n], {n, 0, 23}] (* Jean-François Alcover, Nov 30 2023, after Alois P. Heinz *)

Prog

(PARI) {a(n)=n!*polcoeff(prod(m=1, n, sum(k=0, n\m+1, x^(m*k)/k!^m)+x*O(x^n)), n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A005651.

Sequence in context: A194019 A020017 A060014 * A042659 A054132 A047149

Adjacent sequences: A182663 A182664 A182665 * A182667 A182668 A182669

Keyword

nonn

Author

Paul D. Hanna, Dec 23 2012

Status

approved