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A135749 a(n) = Sum_{k=0..n} binomial(n,k)*(n-k)^k*k^k. 1
1, 1, 3, 19, 217, 3821, 95761, 3214975, 137501505, 7226764921, 455941716481, 33983083953611, 2954163633223969, 296027886705639973, 33823026186790043841, 4363561123325076879991, 630392564294402819207041 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

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

FORMULA

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

MATHEMATICA

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

PROG

(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)

CROSSREFS

Sequence in context: A058165 A074707 A230317 * A005647 A158876 A001833

Adjacent sequences:  A135746 A135747 A135748 * A135750 A135751 A135752

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 27 2007

STATUS

approved

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Last modified February 19 10:34 EST 2019. Contains 320310 sequences. (Running on oeis4.)