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 A322206 G.f.: exp( Sum_{n>=1} A322205(n)*x^n/n ), where A322205(n) is the coefficient of x^(2*n)*y^n/n in Sum_{n>=1} -log(1 - (x^n + y^n)). 2
 1, 1, 4, 14, 63, 294, 1526, 8157, 45332, 257378, 1489539, 8744722, 51965701, 311915649, 1888382937, 11517313486, 70699038868, 436454255701, 2708000234769, 16877547822830, 105614312726477, 663314865710063, 4179789872458354, 26418030929753007, 167435388627981690, 1063892712455899336, 6775891814778961392, 43249097401730644817, 276606084622479837727, 1772391802339441687335, 11376702892986621823617 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Table of n, a(n) for n=0..30. EXAMPLE G.f.: A(x) = 1 + x + 4*x^2 + 14*x^3 + 63*x^4 + 294*x^5 + 1526*x^6 + 8157*x^7 + 45332*x^8 + 257378*x^9 + 1489539*x^10 + 8744722*x^11 + 51965701*x^12 + ... such that log( A(x) ) = x + 7*x^2/2 + 31*x^3/3 + 179*x^4/4 + 1006*x^5/5 + 6265*x^6/6 + 38767*x^7/7 + 245515*x^8/8 + 1562368*x^9/9 + 10017042*x^10/10 + ... + A322205(n)*x^n/n + ... RELATED SERIES. A(x)^3 = 1 + 3*x + 15*x^2 + 67*x^3 + 333*x^4 + 1686*x^5 + 9031*x^6 + 49629*x^7 + 280467*x^8 + 1614932*x^9 + 9449961*x^10 + 56001366*x^11 + 335437797*x^12 + ... PROG (PARI) {L = sum(n=1, 81, -log(1 - (x^n + y^n) +O(x^81) +O(y^81)) ); } {A322205(n) = polcoeff( n*polcoeff( L, 2*n, x), n, y)} {a(n) = polcoeff( exp( sum(m=1, n, A322205(m)*x^m/m ) +x*O(x^n) ), n) } for(n=0, 40, print1( a(n), ", ") ) CROSSREFS Cf. A322200, A322205, A322204. Sequence in context: A050912 A250399 A149494 * A149495 A137956 A357793 Adjacent sequences: A322203 A322204 A322205 * A322207 A322208 A322209 KEYWORD nonn AUTHOR Paul D. Hanna, Dec 01 2018 STATUS approved

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Last modified September 18 08:15 EDT 2024. Contains 375997 sequences. (Running on oeis4.)