A385920
E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^3*A''(x)).
Original entry on oeis.org
1, 1, 3, 34, 1085, 76176, 10075567, 2259237184, 795650626521, 415436957516800, 307467426910853051, 311183690415601457664, 418253671031607891057877, 728624453608629352377831424, 1611758187912750506708147828775, 4448533739124778044473142239512576
Offset: 0
-
terms = 16; A[] = 1; Do[A[x] = Exp[x*A[x]+x^3*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, 2, stirling(2, 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;
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;
A386502
E.g.f. A(x) satisfies A(x) = exp(x + x^4*A'''(x)).
Original entry on oeis.org
1, 1, 1, 1, 25, 3121, 1141921, 967142401, 1632504592321, 4951351715986369, 25004252825639317441, 198308457113999900437441, 2358282522829655305887600961, 40498770303734530275747011026561, 973509226030256545543333641850364737, 31906760631850274511535853878168004240641
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, 3, stirling(3, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A385101
E.g.f. A(x) satisfies A(x) = exp(x * A(x) + x^4/24 * A'''(x)).
Original entry on oeis.org
1, 1, 3, 16, 141, 2161, 59842, 2979509, 258264379, 37321303420, 8597483041421, 3028595626839564, 1572449537786394577, 1165432782899826271026, 1199378312656505145280950, 1673258190849282722438631406, 3099020844849243071430739707913, 7481267275389054589164201426886656
Offset: 0
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terms = 18; A[] = 1; Do[A[x] = Exp[x*A[x]+x^4*A'''[x]/24] + 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)/24)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.