A107100 Numerators of coefficients in g.f. that satisfies: [x^n] A(x)^(1/n) = 0 for all n>1, with a(0)=a(1)=1.

1, 1, 1, -1, -19, 17831, -64667, 1752946877, 796654376069593, -1318782726516512640001, 3482456481351141439684019, -6944717442120502790179764362411651, 32108006354107989164763518257678603933

Offset

0,5

Comments

Sum_{n>=0} a(n) = 2.228747823105104822448312609661581467237449142548497707333713...

Links

Table of n, a(n) for n=0..12.

Example

A(x) = 1 + x + 1/4*x^2 - 1/54*x^3 - 19/4608*x^4 +-...
A(x)^(1/2) = 1 + 1/2*x + 0*x^2 - 1/108*x^3 + 71/27648*x^4 -+...
A(x)^(1/3) = 1 + 1/3*x - 1/36*x^2 + 0*x^3 + 13/13824*x^4 -+...
A(x)^(1/4) = 1 + 1/4*x - 1/32*x^2 + 11/3456*x^3 + 0*x^4 -+...
Initial coefficients of A(x) are:
A107100/A107101 = {1, 1, 1/4, -1/54, -19/4608, 17831/10800000,
-64667/233280000, 1752946877/213462345600000,
796654376069593/71945836874956800000,
-1318782726516512640001/301100369020478344396800000,
3482456481351141439684019/3345559655783092715520000000000, ...}.

Prog

(PARI) {a(n)=local(A=1+x+x^2*O(x^n), C, D); for(k=2, n+1, C=polcoeff((A+t*x^k)^(1/k), k, x); D=(0-subst(C, t, 0))/(subst(C, t, 1)-subst(C, t, 0)); A=A+D*x^k); numerator(polcoeff(A, n))}

Crossrefs

Cf. A107101.

Sequence in context: A186165 A198412 A110392 * A233233 A203581 A125043

Adjacent sequences: A107097 A107098 A107099 * A107101 A107102 A107103

Keyword

frac,sign

Author

Paul D. Hanna, May 12 2005

Status

approved