A306068 G.f. A(x) satisfies: Sum_{n>=0} Product_{k=1..n} x^(n+1-k) + A(x)^k = 1.

-1, 1, -1, -1, 5, -8, -1, 30, -54, -5, 179, -178, -608, 1518, 2611, -18198, 24294, 73472, -365936, 454378, 1238770, -6059472, 7396293, 18989602, -90050185, 97765822, 309199646, -1270466588, 950395782, 5591065880, -17812121981, 3192879156, 107153213918, -255721287314, -142492705829, 2046576827997, -3763046892266, -5107717145521, 37668440369581, -55097197661332, -122428866718927

Offset

1,5

Links

Paul D. Hanna, Table of n, a(n) for n = 1..100

Formula

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

Example

G.f.: A(x) = -x + x^2 - x^3 - x^4 + 5*x^5 - 8*x^6 - x^7 + 30*x^8 - 54*x^9 - 5*x^10 + 179*x^11 - 178*x^12 - 608*x^13 + 1518*x^14 + 2611*x^15 - 18198*x^16 + ...
such that
1  =  1  +  (x + A(x))  +  (x + A(x)^2)*(x^2 + A(x))  +  (x + A(x)^3)*(x^2 + A(x)^2)*(x^3 + A(x))  +  (x + A(x)^4)*(x^2 + A(x)^3)*(x^3 + A(x)^2)*(x^4 + A(x))  +  (x + A(x)^5)*(x^2 + A(x)^4)*(x^3 + A(x)^3)*(x^4 + A(x)^2)*(x^5 + 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, x^(n+1-k) + (x*Ser(A))^k ) ) )[#A+1] ); A[n]}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A306088, A306089.

Sequence in context: A316229 A235936 A260781 * A021949 A363540 A076788

Adjacent sequences: A306065 A306066 A306067 * A306069 A306070 A306071

Keyword

sign

Author

Paul D. Hanna, Jun 23 2018

Status

approved