A381997
E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^4.
Original entry on oeis.org
1, 1, 12, 240, 7328, 303400, 15904032, 1010252320, 75442821120, 6478112692224, 628915387166720, 68121797696449024, 8144844724723482624, 1065508614975814537216, 151392999512027274215424, 23217165210450099377479680, 3822334349865128121165283328, 672407573328393115218009063424
Offset: 0
-
A381997 := proc(n)
n!*add((2*k)^(n-k)*binomial(4*k+1,k)/(4*k+1)/(n-k)!,k=0..n) ;
end proc:
seq(A381997(n),n=0..60) ; # R. J. Mathar, Mar 12 2025
-
a(n) = n!*sum(k=0, n, (2*k)^(n-k)*binomial(4*k+1, k)/((4*k+1)*(n-k)!));
A382000
E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^5.
Original entry on oeis.org
1, 1, 14, 342, 12872, 659280, 42828912, 3375009568, 312860626304, 33361836534144, 4023352486200320, 541461682626399744, 80448618080927609856, 13079749459734097573888, 2309915877337042992324608, 440332184936376095626076160, 90117169223076699520606896128
Offset: 0
A382001
E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^6.
Original entry on oeis.org
1, 1, 16, 462, 20672, 1261400, 97728672, 9190016416, 1016963389696, 129485497897728, 18648682990461440, 2997567408967391744, 531985786683988512768, 103321584851593487961088, 21798243872991807130685440, 4964302861788729054456729600, 1213816740632458735310221672448
Offset: 0
A381999
E.g.f. A(x) satisfies A(x) = 1 + x*exp(2*x)*A(x)^3.
Original entry on oeis.org
1, 1, 10, 156, 3656, 115400, 4595232, 221281312, 12510826624, 812633118336, 59642105050880, 4881685773730304, 440905471531302912, 43559980305765793792, 4673231270870843441152, 541042726968231082967040, 67236501012517546330062848, 8927220151967826907452440576
Offset: 0
Showing 1-4 of 4 results.
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