A306088 G.f. A(x) satisfies: Sum_{n>=0} Product_{k=1..n} x^(n+1-k) - A(x)^k = 1.

1, -1, 3, -7, 19, -56, 177, -580, 1958, -6775, 23895, -85556, 310120, -1135660, 4194795, -15609180, 58456432, -220153594, 833259832, -3167840154, 12091433140, -46318726124, 178014658219, -686199547440, 2652354809685, -10277881815496, 39919204393686, -155378647638728, 605989451550226, -2367789610092956, 9267691579712271, -36333045662257188, 142655905739812690

Offset

1,3

Links

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

Example

G.f.: A(x) = x - x^2 + 3*x^3 - 7*x^4 + 19*x^5 - 56*x^6 + 177*x^7 - 580*x^8 + 1958*x^9 - 6775*x^10 + 23895*x^11 - 85556*x^12 + 310120*x^13 + ...
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)) + ...

Prog

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

Crossrefs

Cf. A306089.

Sequence in context: A147586 A305197 A071716 * A188625 A258171 A263334

Adjacent sequences: A306085 A306086 A306087 * A306089 A306090 A306091

Keyword

sign

Author

Paul D. Hanna, Jun 21 2018

Status

approved