A360987
E.g.f. A(x) satisfies A(x) = exp(x * A(-x)^2).
Original entry on oeis.org
1, 1, -3, -23, 233, 3521, -62171, -1416407, 35880977, 1095318721, -36224195059, -1387587617239, 56675849155705, 2612993427672577, -127090039302776395, -6852033608852338199, 386750643197222855969, 23875394847093826450049
Offset: 0
A168601
E.g.f. A(x) satisfies A(x) = exp( x*A(2*x)^3 ).
Original entry on oeis.org
1, 1, 13, 577, 65737, 17553361, 10704000277, 14796719274961, 46078793355045073, 320622833897384770657, 4940987529761176087132381, 167239138427197351352909547169, 12340269209872740741602975099855641
Offset: 0
E.g.f: A(x) = 1 + x + 13*x^2/2! + 577*x^3/3! + 65737*x^4/4! +...
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{a(n)=local(A=1+x+x*O(x^n)); for(i=0, n, A=exp(x*subst(A, x, 2*x)^3) ); n!*polcoeff(A, n)}
A360989
E.g.f. satisfies A(x) = exp(x / A(-x)^2).
Original entry on oeis.org
1, 1, 5, 1, -231, 81, 55453, -40431, -30313231, 33477985, 29630916981, -43713004191, -45378051616631, 83666428734513, 100216964952070541, -221570666935625999, -301515678925659598623, 777062158771833364929, 1185517627245415533666277
Offset: 0
A360990
E.g.f. satisfies A(x) = exp(x / A(-x)^3).
Original entry on oeis.org
1, 1, 7, -8, -827, 2896, 452179, -2511872, -560237303, 4254259456, 1237434920191, -11907540107264, -4275828959720435, 49800209789734912, 21288959122755516235, -290981680034059649024, -144324916601232035246831, 2264121148389579474141184
Offset: 0
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A360990 := proc(n)
add((-3*n+3*k+1)^(k-1)*(3*k)^(n-k)*binomial(n,k),k=0..n) ;
end proc:
seq(A360990(n),n=0..60) ; # R. J. Mathar, Mar 12 2023
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a(n) = sum(k=0, n, (-3*n+3*k+1)^(k-1)*(3*k)^(n-k)*binomial(n, k));
A385141
E.g.f. A(x) satisfies A(x) = exp(3*x*A(-x)^(1/3)).
Original entry on oeis.org
1, 3, 3, -36, -147, 1728, 14391, -193344, -2572263, 39702528, 744878859, -13061956608, -320684319675, 6310454624256, 192965057926335, -4214431981191168, -155017339047231951, 3722456794316931072, 160513751565607780755, -4204149732317088448512
Offset: 0
A385688
E.g.f. A(x) satisfies A(x) = exp( x*((A(x) + A(-x))/2)^3 ).
Original entry on oeis.org
1, 1, 1, 10, 37, 736, 4861, 145552, 1392553, 55772416, 700205401, 35139710464, 546584937229, 32977620613120, 612127803448981, 43150087404292096, 930914421449463505, 75083676142358560768, 1846230024226716759601, 167681514857730519728128, 4629062510444281987051381
Offset: 0
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terms = 21; A[] = 1; Do[A[x] = Exp[x*((A[x] + A[-x])/2)^3] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Jul 07 2025 *)
Showing 1-6 of 6 results.
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