A385921
E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^4*A'''(x)).
Original entry on oeis.org
1, 1, 3, 16, 509, 66216, 24639367, 21043463344, 35690424280569, 108571039785256960, 549371080081204026731, 4363111116508031602712064, 51938511093491129409954627637, 892615592639462586040781503568896, 21469194967164193484102627607895188975, 703974996795045871424921458192403079479296
Offset: 0
-
terms = 16; A[] = 1; Do[A[x] = Exp[x*A[x]+x^4*A'''[x]] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] * Range[0,terms-1]! (* Stefano Spezia, Aug 04 2025 *)
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+sum(k=1, 3, stirling(3, k, 1)*j^k))*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385922
E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^5*A''''(x)).
Original entry on oeis.org
1, 1, 3, 16, 125, 16296, 11929927, 30230776864, 203634850471929, 3082625458810336000, 93280255561776693446891, 5173509703646410927969711104, 491814532626655136406839912703157, 75968624000349445912469318939348786176, 18252829396078618393615717880609268502659375
Offset: 0
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terms = 15; A[] = 1; Do[A[x] = Exp[x*A[x]+x^5*A''''[x]] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] * Range[0,terms-1]! (* Stefano Spezia, Aug 04 2025 *)
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+sum(k=1, 4, stirling(4, k, 1)*j^k))*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385066
E.g.f. A(x) satisfies A(x) = exp(x + x^3*A''(x)).
Original entry on oeis.org
1, 1, 1, 7, 193, 12481, 1570201, 340513321, 117098181313, 60060238918849, 43839052690362481, 43879747204367814961, 58445034533293136385361, 101048138430710700967252945, 222098609829790469135187472009, 609650270727758340550662998605801, 2058153076335502227178904191401488641
Offset: 0
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=v[i]+sum(j=0, i-1, (1+j)*sum(k=1, 2, stirling(2, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385923
E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^6*A'''''(x)).
Original entry on oeis.org
1, 1, 3, 16, 125, 1296, 949927, 4800957904, 96864153387129, 5860087724767012480, 886162470100464297115691, 294792579950929452096468136704, 196126682670165049397384798842463797, 242323538289386581241948100813652397771776, 523949046624700150687300336366625589891821933775
Offset: 0
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terms = 15; A[] = 1; Do[A[x] = Exp[x*A[x]+x^6*A'''''[x]] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Aug 04 2025 *)
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+sum(k=1, 5, stirling(5, k, 1)*j^k))*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386533
E.g.f. A(x) satisfies A(x) = exp(x * A(x) + x^3/6 * A''(x)).
Original entry on oeis.org
1, 1, 3, 19, 225, 4576, 149517, 7448134, 542269961, 55702422400, 7832607617351, 1468762340728464, 359026336711386577, 112153290859090469184, 44001791667365123420025, 21354097196759712722857776, 12647439446531876144344860113, 9033421564454672567830839315456
Offset: 0
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terms = 18; A[] = 1; Do[A[x] = Exp[x*A[x]+ x^3A''[x]/6] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Aug 04 2025 *)
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a_vector(n) = my(v=vector(n+1)); v[1]=1; for(i=1, n, v[i+1]=sum(j=0, i-1, (1+j)*(1+sum(k=1, 2, stirling(2, k, 1)*j^k)/6)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.