A247075 Expansion of e.g.f.: x^2*G'(x)/G(x)^2, where G(x) satisfies G(x) = x*(1+log(1+G(x))).

1, 0, -1, -2, 12, 96, -220, -7440, -15624, 813120, 7340112, -104165280, -2442773520, 8815815360, 855578733984, 4653629425536, -317564443445760, -5591544140206080, 110965435244017920, 4730495445765296640, -16883238483957574656

Offset: 0

Author

Vladimir Kruchinin, Nov 17 2014

Keywords

• sign

Links

• G. C. Greubel, Table of n, a(n) for n = 0..425

Crossrefs

Cf. A177380.

Programs

Magma

[(&+[Factorial(j)*Binomial(n-1,j)*StirlingFirst(n,j): j in [0..n]]): n in [0..20]]; // G. C. Greubel, Mar 08 2023

Maple

A:= n -> add(k!*binomial(n-1,k)*combinat:-stirling1(n,k),k=0..n):
seq(A(n),n=0..30); # Robert Israel, Nov 17 2014

Mathematica

Table[Sum[StirlingS1[n, k] k! Binomial[n-1, k], {k, 0, n}], {n, 0, 20}] (* Vincenzo Librandi, Nov 17 2014 *)

Maxima

a(n):=sum(k!*binomial(n-1,k)*stirling1(n,k),k,0,n);

SageMath

def A247075(n): return sum( (-1)^(n-k)*factorial(k)*binomial(n-1,k)*stirling_number1(n,k) for k in range(n+1))
[A247075(n) for n in range(21)] # G. C. Greubel, Mar 08 2023

Formula

a(n) = Sum_{k=0..n} k!*binomial(n-1,k)*Stirling1(n,k).

E.g.f.: x^2*G'(x)/G(x)^2 where G(x) = Series_Reversion(x/(1 + log(1+x))); see A177380. - Paul D. Hanna, Nov 17 2014