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 A350525 G.f. A(x) satisfies: [x^(2*n-2)] A(x)^(n*(n+1)/2) = 0 and [x^(2*n-1)] A(x)^(n*(n+1)/2) = 0 for n > 1, with a(0) = 1, a(2) = 6. 1
 1, 6, -36, 360, -4320, 57024, -816480, 12737088, -216950400, 3985853184, -77049957888, 1524488905728, -30107409053184, 576921511037952, -9954313034508288, 94929987120648192, 5615966537573179392, -686220690340602003456, 57421269146260788903936 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,2 LINKS EXAMPLE G.f.: A(x) = 1 + 6*x - 36*x^2 + 360*x^3 - 4320*x^4 + 57024*x^5 - 816480*x^6 + 12737088*x^7 - 216950400*x^8 + 3985853184*x^9 + ... The table of coefficients of x^k in A(x)^(n*(n+1)/2), for k>=0, begins: n=1: [1, 6, -36, 360, -4320, 57024, -816480, 12737088, -216950400, ...]; n=2: [1, 18, 0, 0, 0, 0, -54432, 2659392, -85660416, 2267481600, -...]; n=3: [1, 36, 324, 0, 0, 0, -108864, 3359232, -75582720, 1451188224, ...]; n=4: [1, 60, 1260, 10080, 15120, -36288, 0, 0, 5598720, -245099520, ...]; n=5: [1, 90, 3240, 58320, 524880, 1889568, -272160, -6298560, 0, 0, 0, 0, ...]; ... in which both coefficients of x^(2*n-2) and x^(2*n-1) in A(x)^(n^2) equal zero for n > 1. PROG (PARI) {a(n) = my(A=[1, 6], P); for(i=1, n, A=concat(A, 0); P = (#A+1)\2; A[#A] = -polcoeff( Ser(A)^(P*(P+1)/2)/(P*(P+1)/2), #A-1) ); H=A; A[n+1]} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A250117, A350524. Sequence in context: A053335 A222925 A108733 * A229530 A265474 A277474 Adjacent sequences: A350522 A350523 A350524 * A350526 A350527 A350528 KEYWORD sign AUTHOR Paul D. Hanna, Jan 03 2022 STATUS approved

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Last modified January 29 00:02 EST 2023. Contains 359905 sequences. (Running on oeis4.)