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A135745 E.g.f.: A(x) = Sum_{n>=0} exp((n-1)*x)^n * x^n/n!. 6
1, 1, 1, 7, 49, 501, 6841, 115123, 2362305, 57768553, 1646192881, 53952383871, 2010872281969, 84330050952733, 3945169959883881, 204416253047774251, 11655594262050124801, 727189793270478477777, 49395902623624761264865 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,4

LINKS

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

FORMULA

a(n) = Sum_{k=0..n} C(n,k)*[k*(k-1)]^(n-k).

O.g.f.: Sum_{n>=0} x^n/(1 - n*(n-1)*x)^(n+1). - Paul D. Hanna, Jul 30 2014

MATHEMATICA

Flatten[{1, Table[Sum[Binomial[n, k]*(k*(k - 1))^(n - k), {k, 0, n}], {n, 1, 25}]}] (* G. C. Greubel, Nov 05 2016 *)

PROG

(PARI) {a(n)=sum(k=0, n, binomial(n, k)*(k*(k-1))^(n-k))}

for(n=0, 25, print1(a(n), ", "))

(PARI) {a(n)=n!*polcoeff(sum(k=0, n, exp(k*(k-1)*x +x*O(x^n))*x^k/k!), n)}

for(n=0, 25, print1(a(n), ", "))

(PARI) /* From Sum_{n>=0} x^n/(1 - n*(n-1)*x)^(n+1): */

{a(n)=polcoeff(sum(k=0, n, x^k/(1-k*(k-1)*x +x*O(x^n))^(k+1)), n)}

for(n=0, 25, print1(a(n), ", "))

CROSSREFS

Cf. variants: A135742, A135743, A135744, A135746, A135747.

Sequence in context: A195514 A204211 A125796 * A080895 A047899 A229041

Adjacent sequences:  A135742 A135743 A135744 * A135746 A135747 A135748

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Nov 27 2007

STATUS

approved

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Last modified July 4 14:51 EDT 2020. Contains 335448 sequences. (Running on oeis4.)