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A326599 G.f.: Sum_{n>=0} x^n * (1 + x^n)^n / (1 - x*(1 + x^n))^(n+1). 0

%I #5 Jul 14 2019 00:03:50

%S 1,3,8,19,44,97,207,432,884,1777,3529,6942,13547,26281,50791,97942,

%T 188677,363489,700953,1354060,2621602,5088832,9905382,19335477,

%U 37848971,74287855,146173721,288280956,569715036,1127957956,2236777539,4441749653,8830819362,17574636239,35005944165,69776276002,139165947494

%N G.f.: Sum_{n>=0} x^n * (1 + x^n)^n / (1 - x*(1 + x^n))^(n+1).

%e G.f.: A(x) = 1 + 3*x + 8*x^2 + 19*x^3 + 44*x^4 + 97*x^5 + 207*x^6 + 432*x^7 + 884*x^8 + 1777*x^9 + 3529*x^10 + 6942*x^11 + 13547*x^12 + 26281*x^13 + ...

%e such that

%e A(x) = 1/(1-2*x) + x*(1+x)/(1 - x*(1+x))^2 + x^2*(1+x^2)^2/(1 - x*(1+x^2))^3 + x^3*(1+x^3)^3/(1 - x*(1+x^3))^4 + x^4*(1+x^4)^4/(1 - x*(1+x^4))^5 + x^5*(1+x^5)^5/(1 - x*(1+x^5))^6 + x^6*(1+x^6)^6/(1 - x*(1+x^6))^7 + ...

%o (PARI) {a(n) = my(A = sum(m=0,n, x^m * (1 + x^m +x*O(x^n))^m /(1 - x*(1+x^m) +x*O(x^n))^(m+1) )); polcoeff(A,n)}

%o for(n=0,50,print1(a(n),", "))

%Y Cf. A138247.

%K nonn

%O 0,2

%A _Paul D. Hanna_, Jul 13 2019

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Last modified April 21 04:54 EDT 2024. Contains 371850 sequences. (Running on oeis4.)