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A181071 a(n) = Sum_{k=0..[n/2]} C(n-k,k)^(k+1) * n/(n-k). 5
1, 3, 7, 15, 66, 357, 1891, 20559, 257605, 3436908, 96199478, 2734569969, 96260508267, 6820892444439, 438665726703387, 43006289605790127, 7366025744010911808, 1099005822684238964181, 309398207716948885643749 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

LINKS

Table of n, a(n) for n=1..19.

FORMULA

Logarithmic derivative of A181070.

EXAMPLE

L.g.f.: L(x) = x + 3*x^2/2 + 7*x^3/3 + 15*x^4/4 + 66*x^5/5 +...

which equals the series:

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

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

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

+ (1+ 5^2*x + 10^3*x^2 + 10^4*x^3 + 5^5*x^4 + x^5)*x^5/5

+ (1+ 6^2*x + 15^3*x^2 + 20^4*x^3 + 15^5*x^4 + 6^6*x^5 + x^6)*x^6/6 +...

Exponentiation yields the g.f. of A181070:

exp(L(x)) = 1 + x + 2*x^2 + 4*x^3 + 8*x^4 + 23*x^5 + 88*x^6 + 379*x^7 + 3044*x^8 +...

PROG

(PARI) a(n)=sum(k=0, n\2, binomial(n-k, k)^(k+1)*n/(n-k))

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

CROSSREFS

Cf. A181070 (exp), variants: A181081, A181073.

Sequence in context: A268061 A298358 A023370 * A258936 A096422 A154795

Adjacent sequences:  A181068 A181069 A181070 * A181072 A181073 A181074

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Oct 02 2010

STATUS

approved

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Last modified July 19 12:49 EDT 2019. Contains 325159 sequences. (Running on oeis4.)