A135749 a(n) = Sum_{k=0..n} binomial(n,k)*(n-k)^k*k^k.

1, 1, 3, 19, 217, 3821, 95761, 3214975, 137501505, 7226764921, 455941716481, 33983083953611, 2954163633223969, 296027886705639973, 33823026186790043841, 4363561123325076879991, 630392564294402819207041

Offset: 0

Author

Paul D. Hanna, Nov 27 2007

Keywords

• nonn

Links

• G. C. Greubel, Table of n, a(n) for n = 0..250

Crossrefs

Cf. A000248, A086331, A349965.

Programs

Mathematica

Table[Sum[Binomial[n,k](n-k)^k k^k,{k,n}],{n,0,20}]+1 (* Harvey P. Dale, Oct 08 2012 *)

PARI

a(n)=sum(k=0,n,binomial(n,k)*(n-k)^k*k^k)

PARI

a(n)=n!*polcoeff(sum(k=0,n,exp((n-k)*k*x +x*O(x^n))*x^k/k!),n)

Formula

a(n) = n!*[x^n] Sum_{k=0..n} exp((n-k)*x)^k * x^k/k!.