|
| |
|
|
A325218
|
|
G.f. A(x) satisfies: Sum_{n>=0} x^n * A(x)^(n^2) = Sum_{n>=0} x^(n^2).
|
|
1
|
|
|
|
1, -1, 3, -9, 28, -74, 162, -325, 995, -4734, 15466, 8677, -335037, 703456, 10008733, -77798035, -22911395, 3588683864, -18537404473, -76218346190, 1450216275105, -4631262043579, -57235991842837, 672219894780644, -821654384386424, -40932573680694497, 359643851223904326, 405144935152085312, -31795393797951609594, 220753675876844248793, 938030268510143246068, -27834369944198908535526, 153463296961588410948143, 1346812736734415987235200
(list;
graph;
refs;
listen;
history;
text;
internal format)
|
|
|
|
OFFSET
|
0,3
|
|
|
LINKS
|
|
|
|
EXAMPLE
|
G.f.: A(x) = 1 - x + 3*x^2 - 9*x^3 + 28*x^4 - 74*x^5 + 162*x^6 - 325*x^7 + 995*x^8 - 4734*x^9 + 15466*x^10 + 8677*x^11 - 335037*x^12 + 703456*x^13 + 10008733*x^14 - 77798035*x^15 - 22911395*x^16 + 3588683864*x^17 - 18537404473*x^18 - 76218346190*x^19 + 1450216275105*x^20 + ...
such that
B(x) = 1 + x*A(x) + x^2*A(x)^4 + x^3*A(x)^9 + x^4*A(x)^16 + x^5*A(x)^25 + x^6*A(x)^36 + x^7*A(x)^49 + x^8*A(x)^64 + x^9*A(x)^81 + x^10*A(x)^100 + ...
where
B(x) = 1 + x + x^4 + x^9 + x^16 + x^25 + x^36 + x^49 + x^64 + x^81 + x^100 + ...
|
|
|
PROG
|
(PARI) {a(n) = my(A=[1], SUMSQ = sum(m=0, sqrtint(n+1), x^(m^2)));
for(i=1, n, A=concat(A, 0); A[#A] = -polcoeff( sum(m=0, #A, x^m*Ser(A)^(m^2) ) - SUMSQ, #A); ); H=A; A[n+1]}
for(n=0, 30, print1(a(n), ", "))
|
|
|
CROSSREFS
|
|
|
|
KEYWORD
|
sign
|
|
|
AUTHOR
|
|
|
|
STATUS
|
approved
|
| |
|
|
