A370535 Expansion of g.f. A(x) satisfying A( x^2*(1 + 3*x)*A(x) )^5 = A( x^3*(1 + 5*x)*A(x)^2 )^3.

1, 0, 15, -80, 480, -2832, 16555, -94350, 544050, -3048150, 17177355, -95672700, 530418150, -2927403000, 16080310800, -87976127220, 479790094275, -2607515196300, 14134142487950, -76415523881850, 412207249329390, -2219152192374700, 11925605885527275, -63987288706312050

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..501

Example

G.f.: A(X) = x + 15*x^3 - 80*x^4 + 480*x^5 - 2832*x^6 + 16555*x^7 - 94350*x^8 + 544050*x^9 - 3048150*x^10 + 17177355*x^11 - 95672700*x^12 + ...
where A( x^2*(1 + 3*x)*A(x) )^5 = A( x^3*(1 + 5*x)*A(x)^2 )^3.
RELATED SERIES.
B(x) = A( x^2*(1 + 3*x)*A(x) )^(1/3) = A( x^3*(1 + 5*x)*A(x)^2 )^(1/5)
where B(x) is the g.f. of A370534, which begins
B(x) = x + x^2 + 4*x^3 - 20*x^4 + 100*x^5 - 500*x^6 + 2530*x^7 - 12290*x^8 + 63970*x^9 - 310770*x^10 + 1580415*x^11 - 7901235*x^12 + 39580710*x^13 + ...
B(x)^3 = A( x^2*(1 + 3*x)*A(x) ) = x^3 + 3*x^4 + 15*x^5 - 35*x^6 + 240*x^7 - 1392*x^8 + 8074*x^9 - 44550*x^10 + 262080*x^11 - 1413200*x^12 + ...
B(x)^5 = A( x^3*(1 + 5*x)*A(x)^2 ) = x^5 + 5*x^6 + 30*x^7 - 10*x^8 + 385*x^9 - 2139*x^10 + 13590*x^11 - 80910*x^12 + 515970*x^13 - 2952970*x^14 + ...
B(x)^15 = x^15 + 15*x^16 + 165*x^17 + 995*x^18 + 5805*x^19 + 16083*x^20 + 93075*x^21 - 82575*x^22 + 2166975*x^23 - 11141575*x^24 + 99995160*x^25 + ...
where B(x)^15 = A( x^2*(1 + 3*x)*A(x) )^5 = A( x^3*(1 + 5*x)*A(x)^2 )^3.

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = concat(A, 0); Ax = x*Ser(A);
A[#A] = polcoeff( subst(Ax, x, x^2*(1 + 3*x)*Ax )^5 - subst(Ax, x, x^3*(1 + 5*x)*Ax^2 )^3, #A+14); ); A[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A370536, A370533 (dual), A370437, A370537.

Sequence in context: A024002 A050149 A055815 * A338414 A358917 A244855

Adjacent sequences: A370532 A370533 A370534 * A370536 A370537 A370538

Keyword

sign

Author

Paul D. Hanna, Mar 08 2024

Status

approved