A185082 a(n) = [x^n] G_{n+1}(x) where G_n(x) = F(x*G_n(x)^n) and F(x) = g.f. of A185072 such that [x^n] G_n(x) = 0.

1, 1, 1, 4, 37, 581, 13212, 397090, 14889577, 669865615, 35163845767, 2109590735132, 142351735998715, 10668744913038902, 879070919025078742, 78967715485093873542, 7679624492547098031089, 803723903225549231819755, 90059089612345241265831537

Offset

0,4

Links

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

Example

 Given F(x) is the g.f. of A185072:
F(x) = 1 + x - 2*x^2 + 6*x^3 - 28*x^4 + 70*x^5 - 1446*x^6 - 22302*x^7 -...
then the coefficients in G_n(x) that satisfy G_n(x) = F( x*G_n(x)^n ) begin:
G_1: [(1), 1, -1, 1, -7, -49, -1191, -31569, -1051695, -41520593, ...];
G_2: [1,(1), 0, -1, -6, -78, -1544, -40605, -1328178, -51857806, ...];
G_3: [1, 1,(1), 0, -9, -117, -2118, -53232, -1699905, -65386779, ...];
G_4: [1, 1, 2, (4), 0, -141, -2958, -71900, -2216860, -83454920, ...];
G_5: [1, 1, 3, 11, (37), 0, -3245, -95286, -2941059, -108180433, ...];
G_6: [1, 1, 4, 21, 118, (581), 0, -99086, -3760182, -141280086, ...];
G_7: [1, 1, 5, 34, 259, 2002,(13212), 0, -3775221, -176047295, ...];
G_8: [1, 1, 6, 50, 476, 4788, 47578, (397090), 0, -172383145, ...];
G_9: [1, 1, 7, 69, 785, 9589, 120333, 1468749, (14889577), 0, ...];
G_10:[1, 1, 8, 91, 1202, 17180, 256056, 3859425, 56018694, (669865615), 0, ...]; ...
where the coefficients in parenthesis form this sequence.
Note that the coefficients of x^n in G_n(x) are zero for n>1.
The functions G_n(x) also satisfy F(x) = G_n( x/F(x)^n ).

Prog

 (PARI) {a(n)=local(A=[1, 1]); for(i=1, n, A=concat(A, 0); A[#A]=-Vec((1/x*serreverse(x/Ser(A)^(#A-1)))^(1/(#A-1)))[#A]);
polcoeff((1/x*serreverse(x/Ser(A)^(n+1)))^(1/(n+1)), n)}

Crossrefs

Cf. A185072.

Sequence in context: A349714 A121080 A001518 * A259822 A345102 A036245

Adjacent sequences: A185079 A185080 A185081 * A185083 A185084 A185085

Keyword

nonn

Author

Paul D. Hanna, Jan 22 2012

Status

approved