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A322192
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G.f.: exp( Sum_{n>=1} A322191(n)*x^n/n ), where A322191(n) is the coefficient of x^n*y^n/n in log( Product_{n>=1} 1/(1 - (x^(2*n) - y^(2*n))/(x - y)) ).
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2
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1, 1, 2, 7, 16, 49, 158, 480, 1565, 5372, 18168, 63018, 223069, 790675, 2837099, 10275237, 37365238, 136780746, 503454552, 1860283966, 6903032032, 25710869751, 96062102703, 360005362169, 1352895525992, 5096746479429, 19245661967963, 72829157526334, 276144309118166, 1048989168151209, 3991676310364631, 15213832997014866, 58073559070913632, 221990591912157497, 849708949683300960
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OFFSET
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0,3
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LINKS
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FORMULA
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a(n) ~ c * 4^n / n^(3/2), where c = 0.585811817455537... - Vaclav Kotesovec, Jun 18 2019
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EXAMPLE
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G.f.: A(x) = 1 + x + 2*x^2 + 7*x^3 + 16*x^4 + 49*x^5 + 158*x^6 + 480*x^7 + 1565*x^8 + 5372*x^9 + 18168*x^10 + 63018*x^11 + 223069*x^12 + ...
such that
log( A(x) ) = x + 3*x^2/2 + 16*x^3/3 + 35*x^4/4 + 141*x^5/5 + 528*x^6/6 + 1744*x^7/7 + 6435*x^8/8 + 25225*x^9/9 + 92743*x^10/10 + 352782*x^11/11 + 1364216*x^12/12 + ... + A322191(n)*x^n/n + ...
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PROG
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(PARI) N=35;
{L = sum(n=1, N+1, -log(1 - (x^(2*n) - y^(2*n))/(x-y) +O(x^(2*N+1)) +O(y^(2*N+1))) ); }
{A322191(n) = polcoeff( n*polcoeff( L, n, x), n, y)}
{a(n) = polcoeff( exp( sum(m=1, n, A322191(m)*x^m/m ) +x*O(x^n) ), n) }
for(n=0, N, print1( a(n), ", ") )
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CROSSREFS
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KEYWORD
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nonn
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AUTHOR
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STATUS
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approved
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