A385762
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^3*A''(x)).
Original entry on oeis.org
1, 1, 2, 9, 80, 1204, 27788, 918831, 41389972, 2443323132, 183303840972, 17050267807478, 1926895029660880, 260150110806399232, 41365993162914888760, 7652990621445212758255, 1630131235132495370561820, 396129991240222795968202788, 108937459572870420021782788268
Offset: 0
-
terms = 19; A[] = 0; Do[A[x] = 1/(1-x*A[x]-x^3*A''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 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+sum(k=1, 2, stirling(2, k, 1)*j^k))*v[j+1]*v[i-j])); v;
A385764
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^5*A''''(x)).
Original entry on oeis.org
1, 1, 2, 5, 14, 378, 46500, 16879869, 14229776750, 23948731244678, 72492823741526156, 365581334105823084634, 2896500982661242290253612, 34419121542689992919239814260, 590735385934420874267059790772360, 14193599152271246770955912922939691797, 465024889616667096875210999651863472880846
Offset: 0
-
terms = 17; A[] = 0; Do[A[x] = 1/(1-x*A[x]-x^5*A''''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 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+sum(k=1, 4, stirling(4, k, 1)*j^k))*v[j+1]*v[i-j])); v;
A385765
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^6*A'''''(x)).
Original entry on oeis.org
1, 1, 2, 5, 14, 42, 5172, 3739389, 9434483630, 63428037194102, 959222215928392076, 29009757539769286481866, 1608387988236777669667251772, 152866019594999736359695792369300, 23609086665918990295149462904374925800, 5671917808033245221993631555503554148332485
Offset: 0
-
terms = 16; A[] = 0; Do[A[x] = 1/(1-x*A[x]-x^6*A'''''[x]) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 09 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+sum(k=1, 5, stirling(5, k, 1)*j^k))*v[j+1]*v[i-j])); v;
A385831
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^3) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 32, 961, 64467, 8255248, 1808137854, 625644428013, 322212826476551, 235861774406899499, 236570361788785389414, 315585587694401993913716, 546279374467805677562555764, 1201815582876341559500261276952, 3301389061225358326490572037897646
Offset: 0
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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^3)*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 *)
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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;
A386449
G.f. A(x) satisfies A(x) = 1/(1 - x - x^4*A'''(x)).
Original entry on oeis.org
1, 1, 1, 1, 7, 181, 11215, 1368049, 290015209, 98023774645, 49599740115757, 35810914359761065, 35524377449180431975, 46963191178201310535625, 80682726920407341929523811, 176372394085267937467487988481, 481849299958664384125278899595601, 1619977170089211596368385150640702601
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, sum(k=1, 3, stirling(3, k, 1)*j^k)*v[j+1]*v[i-j])); v;
Showing 1-6 of 6 results.