A306087 G.f. A(x) satisfies: Sum_{n>=0} Product_{k=1..n} (n+1-k)*x + k*A(x) = 1.

-1, 1, -1, -2, 8, 56, -281, -3061, 18612, 271129, -1925781, -34967550, 284063311, 6174304311, -56535769915, -1431894779510, 14610783773266, 422789237646634, -4761801655073506, -155050750819877478, 1911855043475987609, 69202778917256845631, -927610459464373932427, -36955258706329671973028, 535191096878546873823897, 23273612576939618406997055, -362206459402896340382856127

Offset

1,4

Links

Paul D. Hanna, Table of n, a(n) for n = 1..150

Formula

G.f. A(x) satisfies: A(A(x)) = x.

Example

G.f.: A(x) = -x + x^2 - x^3 - 2*x^4 + 8*x^5 + 56*x^6 - 281*x^7 - 3061*x^8 + 18612*x^9 + 271129*x^10 - 1925781*x^11 - 34967550*x^12 + 284063311*x^13 + 6174304311*x^14 - 56535769915*x^15 - 1431894779510*x^16 + ...
such that
1  =  1  +  (x + A(x))  +  (x + 2*A(x))*(2*x + A(x))  +  (x + 3*A(x))*(2*x + 2*A(x))*(3*x + A(x))  +  (x + 4*A(x))*(2*x + 3*A(x))*(3*x + 2*A(x))*(4*x + A(x))  +  (x + 5*A(x))*(2*x + 4*A(x))*(3*x + 3*A(x))*(4*x + 2*A(x))*(5*x + A(x)) + ...
also, A(A(x)) = x.

Prog

(PARI) {a(n) = my(A=[-1]); for(i=1, n, A = concat(A, 0); A[#A] = -Vec( sum(n=0, #A, prod(k=1, n, (n+1-k)*x + (k)*x*Ser(A) ) ) )[#A+1] ); A[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A306090.

Sequence in context: A023179 A009298 A354175 * A113248 A353611 A333564

Adjacent sequences: A306084 A306085 A306086 * A306088 A306089 A306090

Keyword

sign

Author

Paul D. Hanna, Jun 23 2018

Status

approved