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A181083 a(n) = Sum_{k=0..[n/2]} C(n-k,k)^n * n/(n-k). 2
1, 3, 13, 111, 1686, 88737, 14355265, 3583775847, 1789371713317, 4311992850152298, 23667113846872049808, 185391762466214524964649, 4305238471804328835068596175, 468653724243371951619336632177235 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..14.

FORMULA

L.g.f.: L(x) = Sum_{n>=1} [Sum_{k=0..n} C(n,k)^(n+k)*x^k] * x^n/n.

Logarithmic derivative of A181082.

EXAMPLE

L.g.f.: L(x) = x + 3*x^2/2 + 13*x^3/3 + 111*x^4/4 + 1686*x^5/5 +...

which equals the series:

L(x) = (1 + x)*x + (1 + 2^3*x + x^2)*x^2/2

+ (1+ 3^4*x + 3^5*x^2 + x^3)*x^3/3

+ (1+ 4^5*x + 6^6*x^2 + 4^7*x^3 + x^4)*x^4/4

+ (1+ 5^6*x + 10^7*x^2 + 10^8*x^3 + 5^9*x^4 + x^5)*x^5/5

+ (1+ 6^7*x + 15^8*x^2 + 20^9*x^3 + 15^10*x^4 + 6^11*x^5 + x^6)*x^6/6 +...

Exponentiation yields the g.f. of A181082:

exp(L(x)) = 1 + x + 2*x^2 + 6*x^3 + 34*x^4 + 375*x^5 + 15200*x^6 + 2066401*x^7 +...

MATHEMATICA

Table[Sum[Binomial[n-k, k]^n n/(n-k), {k, 0, Floor[n/2]}], {n, 20}] (* Harvey P. Dale, Jun 24 2015 *)

PROG

(PARI) a(n)=sum(k=0, n\2, binomial(n-k, k)^n*n/(n-k))

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

CROSSREFS

Cf. A181082 (exp), variants: A181081, A181071, A166895.

Sequence in context: A222863 A223911 A006860 * A090537 A063269 A105431

Adjacent sequences:  A181080 A181081 A181082 * A181084 A181085 A181086

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 02 2010

STATUS

approved

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Last modified February 17 18:46 EST 2019. Contains 320222 sequences. (Running on oeis4.)