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A265267
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E.g.f.: exp(-2) * Sum_{n>=0} 2^n * (1+x)^(n^2) / n!.
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0
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1, 6, 88, 2160, 76336, 3594112, 214575872, 15695861760, 1371486918144, 140382841170944, 16572993648603136, 2228162239340027904, 337576082591565651968, 57121976918741964259328, 10713284121614206013898752, 2212342319434677836830015488, 500118162321472987555560620032, 123128345425943590420826294059008, 32864579386892803455158341264736256
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OFFSET
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0,2
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LINKS
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EXAMPLE
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E.g.f.: A(x) = 1 + 6*x + 88*x^2/2! + 2160*x^3/3! + 76336*x^4/4! + 3594112*x^5/5! + 214575872*x^6/6! + 15695861760*x^7/7! + 1371486918144*x^8/8! +...
where
A(x)*exp(2) = 1 + 2*(1+x) + 2^2*(1+x)^4/2! + 2^3*(1+x)^9/3! + 2^4*(1+x)^16/4! + 2^5*(1+x)^25/5! + 2^6*(1+x)^36/6! + 2^7*(1+x)^49/7! + 2^8*(1+x)^64/8! +...
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PROG
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(PARI) /* Quick print of terms 0..30: */
\p80
Vec(round( serlaplace( sum(n=0, 400, 2^n * (1+x +O(x^31))^(n^2) /n! *1.)/exp(2) ) ))
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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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