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 A262940 G.f. satisfies: [x^n] A(x)^(2^m) = 2^m, where m = A007814(n+1) is the highest exponent of 2 dividing n+1, for n>=0. 2
 1, 1, 1, -3, 1, 3, 1, 21, 1, -21, 1, 255, 1, -255, 1, 478677, 1, -478677, 1, 7152407, 1, -7152407, 1, -1291535081, 1, 1291535081, 1, -21021866227, 1, 21021866227, 1, 8367123104756933, 1, -8367123104756933, 1, 125486744208053623, 1, -125486744208053623, 1, -22639240870533272321, 1, 22639240870533272321, 1, -368298497943774746859, 1, 368298497943774746859, 1, -1120119534438107659394201, 1, 1120119534438107659394201 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,4 LINKS Paul D. Hanna, Table of n, a(n) for n = 0..1024 FORMULA a(2*n) = 1 for n>=0. a(4*n+1) = -a(4*n-1) for n>0. Coefficient of x^k in A(x)^(2^n) equals 2^n at k = m*2^(n+1) + 2^n - 1 for m>=0. EXAMPLE G.f.: A(x) = 1 + x + x^2 - 3*x^3 + x^4 + 3*x^5 + x^6 + 21*x^7 + x^8 - 21*x^9 + x^10 + 255*x^11 + x^12 - 255*x^13 + x^14 + 478677*x^15 + x^16 +... The coefficients in A(x)^n begin: n=1: [1, 1, 1, -3, 1, 3, 1, 21, 1, -21, 1, 255, ...]; n=2: [1, 2, 3, -4, -3, 2, 19, 44, 29, 2, -153, 512, ...]; n=3: [1, 3, 6, -2, -9, -9, 40, 102, 117, 51, -354, 504, ...]; n=4: [1, 4, 10, 4, -13, -32, 44, 200, 341, 220, -586, 4, ...]; n=5: [1, 5, 15, 15, -10, -64, 10, 310, 775, 755, -679, -1305, ...]; n=6: [1, 6, 21, 32, 6, -96, -78, 372, 1443, 2030, -45, -3528, ...]; n=7: [1, 7, 28, 56, 42, -112, -224, 302, 2275, 4459, 2520, -5852, ...]; n=8: [1, 8, 36, 88, 106, -88, -412, 8, 3075, 8352, 8888, -5568, ...]; ... where the coefficient of x^k in A(x)^(2^m) = 2^m where m = A007814(k+1) for k>=0, like so: [x^0] A(x)^1 = 1; [x^1] A(x)^2 = 2; [x^2] A(x)^1 = 1; [x^3] A(x)^4 = 4; [x^4] A(x)^1 = 1; [x^5] A(x)^2 = 2; [x^6] A(x)^1 = 1; [x^7] A(x)^8 = 8; ... PROG (PARI) {a(n) = local(A=[1, 1]); for(k=3, n+1, A=concat(A, 0); m=2^valuation(k, 2); A[k] = 1 - Vec(Ser(A)^m)[k]/m ); A[n+1]} for(n=0, 64, print1(a(n), ", ")) CROSSREFS Cf. A262939. Sequence in context: A079412 A356655 A306861 * A278601 A281038 A263677 Adjacent sequences: A262937 A262938 A262939 * A262941 A262942 A262943 KEYWORD sign,look AUTHOR Paul D. Hanna, Oct 04 2015 STATUS approved

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Last modified August 12 09:11 EDT 2024. Contains 375085 sequences. (Running on oeis4.)