A371524
E.g.f. A(x) satisfies A(x) = exp( 2 * x * (1 + A(x)^(1/4)) ).
Original entry on oeis.org
1, 4, 20, 124, 936, 8424, 88648, 1072432, 14702720, 225692128, 3839770656, 71780577312, 1463532416320, 32337850727680, 770039603953664, 19664621381714944, 536234348295180288, 15554459021934423552, 478297493455731968512, 15543431292269887979008
Offset: 0
-
my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(2*x-4*lambertw(-x/2*exp(x/2)))))
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a(n, r=2, t=0, u=1/2) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
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my(N=20, x='x+O('x^N)); Vec(2*sum(k=0, N, (k/2+2)^(k-1)*x^k/(1-(k/2+2)*x)^(k+1)))
A372235
E.g.f. A(x) satisfies A(x) = exp( x * (1 + A(x)^(3/2)) ).
Original entry on oeis.org
1, 2, 10, 98, 1456, 29132, 734932, 22407464, 801710560, 32940601424, 1528816004944, 79109107128944, 4516145972879680, 281970941337424640, 19114791434098402816, 1398205517746364523008, 109771912847021666795008, 9206931548976575570314496
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-2/3*lambertw(-3*x/2*exp(3*x/2)))))
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a(n, r=1, t=0, u=3/2) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (3*k/2+1)^(k-1)*x^k/(1-(3*k/2+1)*x)^(k+1)))
A372246
E.g.f. A(x) satisfies A(x) = exp( x * A(x) * (1 + A(x)^(1/2)) ).
Original entry on oeis.org
1, 2, 14, 182, 3528, 91572, 2988124, 117646664, 5429848160, 287596190960, 17197966810224, 1146212005029456, 84257333026857472, 6772618660901287040, 590968891266018673664, 55635634440230961625088, 5621016808791883758841344, 606656453852999167732922112
Offset: 0
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a(n, r=1, t=1, u=1/2) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
A372278
E.g.f. A(x) satisfies A(x) = exp( x * (1 + A(x)^(5/2)) ).
Original entry on oeis.org
1, 2, 14, 218, 5256, 172332, 7161964, 360849848, 21378442976, 1456505344592, 112197636802224, 9643110922761648, 914870017865191936, 94969006015521439232, 10707303771557931935744, 1302965738334245437242368, 170216425515761065556430336
Offset: 0
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my(N=20, x='x+O('x^N)); Vec(serlaplace(exp(x-2/5*lambertw(-5*x/2*exp(5*x/2)))))
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a(n, r=1, t=0, u=5/2) = r*sum(k=0, n, (t*n+u*k+r)^(n-1)*binomial(n, k));
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my(N=20, x='x+O('x^N)); Vec(sum(k=0, N, (5*k/2+1)^(k-1)*x^k/(1-(5*k/2+1)*x)^(k+1)))
Showing 1-4 of 4 results.