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A118795 E.g.f.: -1 + exp(( 1 - sqrt(5 - 4*exp(x)) )/2). 2
0, 1, 4, 29, 329, 5172, 104335, 2571473, 74894818, 2516911731, 95862252417, 4080739041238, 192000366357981, 9894168501171229, 554208686184384028, 33527021385789228265, 2178482569432714859789, 151314182463701892157460, 11188187745418763137485747 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

COMMENTS

Also equals the unsigned row sums of triangle A118793 (offset without leading zero).

LINKS

Table of n, a(n) for n=0..18.

FORMULA

a(n) = (n-1)!*Sum_{k=0..n-1} abs( [x^k] (x/log(1-x-x^2))^n/(n-1-k)! ) for n>0.

a(n) = sum(k=1..n, (sum(i=0..n-k, ((i+k-1)!*C(k+2*i-1,i+k-1) *stirling2(n, i+k))))/(k-1)!). - Vladimir Kruchinin, Nov 22 2011

a(n) ~ sqrt(5) * n^(n-1) / (2^(3/2) * exp(n-1/2) * (log(5/4))^(n-1/2)). - Vaclav Kotesovec, Jul 14 2014

EXAMPLE

E.g.f.: A(x) = x + (4/2)*x^2 + (29/6)*x^3 + (329/24)*x^4 + (5172/120)*x^5 + ...

MATHEMATICA

CoefficientList[Series[-1 + E^((1-Sqrt[5-4*E^x])/2), {x, 0, 20}], x] * Range[0, 20]! (* Vaclav Kotesovec, Jul 14 2014 *)

PROG

(PARI) a(n)=local(x=X+X^2*O(X^n)); n!*polcoeff(-1+exp((1-sqrt(5-4*exp(x)))/2), n, X)

(PARI) /* As the unsigned row sums of A118793: */ a(n)=local(x=X+X^2*O(X^n)); if(n<1, 0, (n-1)!*sum(k=0, n-1, abs(polcoeff(((x/log(1-x-x^2)))^n/(n-1-k)!, k, X))))

(Maxima) a(n):=sum((sum(((i+k-1)!*binomial(k+2*i-1, i+k-1)*stirling2(n, i+k)), i, 0, n-k))/(k-1)!, k, 1, n); /* Vladimir Kruchinin, Nov 22 2011 */

CROSSREFS

Cf. A118793, A118794.

Sequence in context: A215955 A295237 A028853 * A325478 A099700 A305636

Adjacent sequences:  A118792 A118793 A118794 * A118796 A118797 A118798

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Apr 30 2006

STATUS

approved

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Last modified May 26 01:32 EDT 2022. Contains 354073 sequences. (Running on oeis4.)