A377258 G.f. A(x) satisfies A(x)^7 = A(x^7) + 7*A(x^8).

1, 1, -3, 13, -65, 351, -1989, 11650, -69900, 427168, -2648444, 16612986, -105215708, 671762688, -4318480068, 27926208102, -181520595372, 1185224306328, -7769814296892, 51117268739082, -337374433220892, 2233100488061696, -14819687150440940, 98583271355649642, -657222710894636084

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..1000

Example

G.f.: A(x) = x + x^2 - 3*x^3 + 13*x^4 - 65*x^5 + 351*x^6 - 1989*x^7 + 11650*x^8 - 69900*x^9 + 427168*x^10 - 2648444*x^11 + 16612986*x^12 + ...
A(x)^7 = x^7 + 7*x^8 + x^14 + 7*x^16 - 3*x^21 - 21*x^24 + 13*x^28 + 91*x^32 - 65*x^35 - 455*x^40 + 351*x^42 + 2457*x^48 - 1989*x^49  - 2273*x^56 - 69900*x^63 + ...
where A(x)^7 = A(x^7) + 7*A(x^8).
SPECIFIC VALUES.
A(1/7) = 0.15772708901641335150527781783735289338509817552641...
  where A(1/7)^7 = A(1/7^7) + 7*A(1/7^8).
A(1/8) = 0.13674460851389170274849954118414318282336460429579...
  where A(1/8)^7 = A(1/8^7) + 7*A(1/8^8).
A(1/9) = 0.12062970906064325012650139044513082950987815459592...
  where A(1/9)^7 = A(1/9^7) + 7*A(1/9^8).

Prog

(PARI) {a(n) = my(A, V=[0, 1]); for(i=1, n+1, V=concat(V, 0); A=Ser(V);
V[#V] = polcoef( (subst(A, x, x^7) + 7*subst(A, x, x^8) - A^7 )/7, #V+5) ); polcoef(A, n)}
for(n=1, 50, print1(a(n), ", "))

Crossrefs

Cf. A377255, A377256, A377257.

Sequence in context: A106227 A352705 A352706 * A368973 A256332 A284715

Adjacent sequences: A377255 A377256 A377257 * A377259 A377260 A377261

Keyword

sign

Author

Paul D. Hanna, Dec 01 2024

Status

approved