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;
A385833
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^5) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 104, 25585, 26276091, 82191698776, 639369308538270, 10747798328839679301, 352216100969784522738455, 20799065226839989441184616755, 2079968920938449464603267217930862, 334987314655287149221766445992266495796, 83356568448492338030736248231384628286761124
Offset: 0
-
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^5)*v[j+1]*v[i-j])); v;
A385763
G.f. A(x) satisfies A(x) = 1/(1 - x*A(x) - x^4*A'''(x)).
Original entry on oeis.org
1, 1, 2, 5, 44, 1188, 74880, 9211479, 1962123260, 665169218468, 337242780292376, 243827199998597254, 242120748323922920272, 320325994582940359050400, 550640627320172764415124000, 1204251372776149567847238889047, 3291219553094816112273747054673476
Offset: 0
-
terms = 17; A[] = 0; Do[A[x] = 1/(1-x*A[x]-x^4*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, 3, stirling(3, 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;
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;
A386451
G.f. A(x) satisfies A(x) = 1/(1 - x - x^6*A'''''(x)).
Original entry on oeis.org
1, 1, 1, 1, 1, 1, 121, 87361, 220324321, 1481019998401, 22395984195495601, 677299352559157967041, 37550830682188851813205921, 3568906049019293501471580099841, 551188987985086896272084982413188201, 132418744847944340085178947237195978556801, 47718683730343729293790168893699493431209021761
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, 5, stirling(5, k, 1)*j^k)*v[j+1]*v[i-j])); v;
Showing 1-6 of 6 results.