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A201795 E.g.f. satisfies: A(x)+1/2*A(x)^2 = x*exp(A(x)). 0
1, 1, 3, 13, 80, 621, 5887, 65689, 844587, 12289825, 199702646, 3584177829, 70418168977, 1503204079573, 34644744039375, 857391850897201, 22677415997829788, 638386960029846921, 19057447729907765407, 601346850250707128125 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,3

LINKS

Table of n, a(n) for n=1..20.

FORMULA

a(n) = n!*T(n,1), T(n,m) = sum(k=1..n-m, T(n-m,k)*m^k/k!-binomial(m,k)/2^k*T(n,k+m))), n>m, with T(n,n)=1.

a(n) = ((n-1)!*sum(k=1..n-1, C(n+k-1,n-1)*sum(j=1..k, (-1)^(j)*C(k,j) *sum(i=0..n-1, ((-1)^i*j^i*C(j,n-i-1)*2^(-n+i+1))/i!)))), n>1, a(n)=1. - Vladimir Kruchinin, Feb 24 2012

a(n) ~ 2^(-1/4) * exp((sqrt(2)-1)*n) * (sqrt(2)-1)^(n-1/2) * n^(n-1). - Vaclav Kotesovec, Aug 04 2014

MATHEMATICA

Rest[CoefficientList[InverseSeries[Series[(x*(2 + x))/(2*E^x), {x, 0, 20}], x], x] * Range[0, 20]!] (* Vaclav Kotesovec, Aug 04 2014 *)

PROG

(Maxima)

array(B, 100, 100);

fillarray (B, makelist (-1, i, 1, 1000));

T(n, m):=if B[n, m]=-1 then BB[n, m]:(if n=m then 1 else sum(T(n-m, k)*m^k/k!-binomial(m, k)/2^k*T(n, k+m), k, 1, n-m)) else B[n, m];

makelist(n!*T(n, 1), n, 1, 20);

a(n):=if n=1 then 1 else ((n-1)!*sum(binomial(n+k-1, n-1) *sum((-1)^(j) *binomial(k, j)*sum(((-1)^i*j^i*binomial(j, n-i-1) *2^(-n+i+1))/i!, i, 0, n-1), j, 1, k), k, 1, n-1)); [From Vladimir Kruchinin, Feb 24 2012]

CROSSREFS

Sequence in context: A112935 A258377 A335636 * A308521 A183278 A331643

Adjacent sequences:  A201792 A201793 A201794 * A201796 A201797 A201798

KEYWORD

nonn

AUTHOR

Vladimir Kruchinin, Dec 05 2011

STATUS

approved

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Last modified April 22 16:32 EDT 2021. Contains 343177 sequences. (Running on oeis4.)