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A235802 E.g.f.: 1/(1 - x)^(2/(2-x)). 0
1, 1, 3, 12, 61, 375, 2697, 22176, 204977, 2102445, 23685615, 290642220, 3857751573, 55063797243, 840956549517, 13682498891040, 236257301424225, 4314883836968505, 83102361300891963, 1683252077760375660, 35770269996769203405, 795749735451309432255 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..21.

FORMULA

E.g.f.: exp( Sum_{n>=1} x^n/n * Sum_{k=0..n-1} 1/C(n-1,k) ).

E.g.f.: exp( Sum_{n>=1} A003149(n-1)*x^n/n! ), where A003149(n) = Sum_{k=0..n} k!*(n-k)!.

a(n) ~ n! * (n-2*log(n)). - Vaclav Kotesovec, Jul 13 2014

EXAMPLE

E.g.f.: A(x) = 1 + 2*x + 12*x^2/2! + 96*x^3/3! + 976*x^4/4! + 12000*x^5/5! +...

where the logarithm involves sums of reciprocal binomial coefficients:

log(A(x)) = x*(1) + x^2/2*(1 + 1) + x^3/3*(1 + 1/2 + 1) + x^4/4*(1 + 1/3 + 1/3 + 1) + x^5/5*(1 + 1/4 + 1/6 + 1/4 + 1) + x^6/6*(1 + 1/5 + 1/10 + 1/10 + 1/5 + 1) +...

Explicitly, the logarithm begins:

log(A(x)) = x + 2*x^2/2! + 5*x^3/3! + 16*x^4/4! + 64*x^5/5! + 312*x^6/6! + 1812*x^7/7! + 12288*x^8/8! +...+ A003149(n-1)*x^n/n! +...

MATHEMATICA

CoefficientList[Series[1/(1-x)^(2/(2-x)), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 13 2014 *)

PROG

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

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

(PARI) {a(n)=n!*polcoeff(1/(1-x+x*O(x^n))^(2/(2-x)), n)}

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

CROSSREFS

Cf. A193425, A003149.

Sequence in context: A182970 A159925 A331607 * A317169 A121694 A331616

Adjacent sequences:  A235799 A235800 A235801 * A235803 A235804 A235805

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Jan 15 2014

STATUS

approved

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Last modified December 2 03:22 EST 2020. Contains 338865 sequences. (Running on oeis4.)