A381142
Expansion of e.g.f. exp( -LambertW(-sin(x)) ).
Original entry on oeis.org
1, 1, 3, 15, 113, 1137, 14355, 218239, 3883585, 79218721, 1822842243, 46717337007, 1319891043569, 40759239427857, 1365932381706963, 49373610759452575, 1914856819983977473, 79316216447375396161, 3494800326874932467331, 163218136611270923087439
Offset: 0
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a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (k+1)^(k-1)*I^(n-k)*a136630(n, k));
A381145
Expansion of e.g.f. (1/x) * Series_Reversion( x * exp(-sin(x)) ).
Original entry on oeis.org
1, 1, 3, 15, 105, 937, 10059, 124607, 1720593, 25578001, 391041299, 5628440015, 55397475705, -847789025159, -93469767131685, -5040670692970753, -236210967512228575, -10629917015586704351, -475183316832486106589, -21394016956935371375601, -975459739630268065696887
Offset: 0
-
a136630(n, k) = 1/(2^k*k!)*sum(j=0, k, (-1)^(k-j)*(2*j-k)^n*binomial(k, j));
a(n) = sum(k=0, n, (n+1)^(k-1)*I^(n-k)*a136630(n, k));
A385427
E.g.f. A(x) satisfies A(x) = exp( arcsin(x * A(x)) / A(x) ).
Original entry on oeis.org
1, 1, 1, 2, 13, 100, 861, 9536, 127737, 1938896, 33240185, 639683552, 13601898245, 316356906944, 7998251969813, 218420230243840, 6405441641302641, 200779795515236608, 6699317212660139761, 237070134772942395904, 8868209937245857514365, 349657703494298519409664
Offset: 0
-
nmax = 20; A[] = 1; Do[A[x] = E^(ArcSin[x*A[x]]/A[x]) + O[x]^j // Normal, {j, 1, nmax + 1}]; CoefficientList[A[x], x] * Range[0, nmax]! (* Vaclav Kotesovec, Jul 05 2025 *)
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a385343(n, k) = my(x='x+O('x^(n+1))); n!*polcoef(asin(x)^k/k!, n);
a(n) = sum(k=0, n, (n-k+1)^(k-1)*a385343(n, k));
Showing 1-3 of 3 results.