A213357 E.g.f. satisfies A(x) = 1 + (exp(x) - 1) * A(exp(x) - 1).

1, 1, 3, 16, 133, 1561, 24374, 485640, 11969843, 356348290, 12572687675, 517644938724, 24553141710156, 1327223189312606, 81005220402829714, 5537660009982114858, 421050946315817655785, 35387457515051683169307, 3269500807582223015227780

Offset

0,3

Links

Vincenzo Librandi, Table of n, a(n) for n = 0..200

Formula

a(n) = Sum_{k=1..n} k * a(k-1) * Stirling2(n, k) if n>0.

A048801(n) = n * a(n-1) = Sum_{k=1..n} a(k) * Stirling1(n, k) if n>0.

Example

1 + x + 3*x^2 + 16*x^3 + 133*x^4 + 1561*x^5 + 24374*x^6 + 485640*x^7 + ...

Mathematica

nmax=20; b = ConstantArray[0, nmax+1]; b[[1]]=1; Do[b[[n+1]] = Sum[k*b[[k]]*StirlingS2[n, k], {k, 1, n}], {n, 1, nmax-1}]; b (* Vaclav Kotesovec, Mar 12 2014 *)

Prog

(PARI) {a(n) = local(A); if( n<0, 0, A = 1 + O(x); for( k=1, n, A = subst( 1 + x * A, x, exp( x + x * (A - A)) - 1)); n! * polcoeff( A, n))}
(PARI) a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=1, i, j*stirling(i, j, 2)*v[j])); v; \\ Seiichi Manyama, Jun 04 2022

Crossrefs

Cf. A048801, A135750.

Sequence in context: A341852 A141628 A048802 * A119392 A307979 A129043

Adjacent sequences: A213354 A213355 A213356 * A213358 A213359 A213360

Keyword

nonn

Author

Michael Somos, Jun 09 2012

Status

approved