A167007 G.f.: A(x) = exp( Sum_{n>=1} A167010(n)*x^n/n ) where A167010(n) = Sum_{k=0..n} binomial(n,k)^n.

1, 2, 5, 26, 501, 42262, 14564184, 18926665052, 96371663657380, 1825266130738144920, 136764680697906838980633, 38133043109557952095731186822, 42464330390232136488003531922964743

Offset

0,2

Links

G. C. Greubel, Table of n, a(n) for n = 0..59

Formula

a(n) = (1/n)*Sum_{k=1..n} A167010(k)*a(n-k) for n>0 with a(0)=1. - Paul D. Hanna, Nov 25 2009

Example

G.f.: A(x) = 1 + 2*x + 5*x^2 + 26*x^3 + 501*x^4 + 42262*x^5 + ...
log(A(x)) = 2*x + 6*x^2/2 + 56*x^3/3 + 1810*x^4/4 + 206252*x^5/5 + 86874564*x^6/6 + ... + A167010(n)*x^n/n + ...

Mathematica

A167010[n_]:= A167010[n]= Sum[Binomial[n, j]^n, {j, 0, n}];
A167007[n_]:= A167007[n]= If[n==0, 1, (1/n)*Sum[A167010[j]*A167007[n-j], {j, n}]];
Table[A167007[n], {n, 0, 30}] (* G. C. Greubel, Aug 26 2022 *)

Prog

(PARI) {a(n) = polcoeff(exp(sum(m=1, n, sum(k=0, m, binomial(m, k)^m)*x^m/m) +x*O(x^n)), n)};
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, sum(j=0, k, binomial(k, j)^k)*a(n-k)))} \\ Paul D. Hanna, Nov 25 2009
(Magma)
A167010:= func< n | (&+[Binomial(n, j)^n: j in [0..n]]) >;
function A167007(n)
  if n lt 2 then return n+1;
  else return (&+[A167010(j)*A167007(n-j): j in [1..n]])/n;
  end if; return A167007;
end function;
[A167007(n): n in [0..20]]; // G. C. Greubel, Aug 26 2022
(SageMath)
def A167010(n): return sum(binomial(n, j)^n for j in (0..n))
def A167007(n): return 1 if (n==0) else (1/n)*sum( A167010(j)*A167007(n-j) for j in (1..n))
[A167007(n) for n in (0..30)] # G. C. Greubel, Aug 26 2022

Crossrefs

Cf. A155200, A167006, A167010.

Sequence in context: A323293 A258868 A322705 * A064006 A003095 A023362

Adjacent sequences: A167004 A167005 A167006 * A167008 A167009 A167010

Keyword

nonn

Author

Paul D. Hanna, Nov 17 2009

Status

approved