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 *)
-
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;
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 *)
-
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;
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
-
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 *)
-
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;
A386503
E.g.f. A(x) satisfies A(x) = exp(x + x^5*A''''(x)).
Original entry on oeis.org
1, 1, 1, 1, 1, 121, 87841, 221971681, 1493423016961, 22593988839985921, 683468095232158346881, 37898988106295372711276161, 3602374572375663444650415755521, 556397556871212729711470761587498241, 133676738300734051631377763872501373230081, 48173754506706929414138973409107160269088573441
Offset: 0
-
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, 4, stirling(4, k, 1)*j^k)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386534
E.g.f. A(x) satisfies A(x) = exp(x * A(x) + x^5/120 * A''''(x)).
Original entry on oeis.org
1, 1, 3, 16, 125, 1421, 26833, 968626, 70638465, 10215072856, 2782227253373, 1347216023489436, 1099522113403916545, 1443781044602756539876, 2930977624516859360997387, 8889808786962394898290294048, 39115513670641030174644662148305, 243377943140592361750259305827057888
Offset: 0
-
terms = 18; A[] = 1; Do[A[x] = Exp[x*A[x]+x^5*A''''[x]/120] + O[x]^terms // Normal, terms]; CoefficientList[A[x], x]Range[0,terms-1]! (* Stefano Spezia, Aug 04 2025 *)
-
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)/120)*binomial(i-1, j)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.