A385758
G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^3*A''(x))).
Original entry on oeis.org
1, 2, 5, 25, 241, 3850, 92699, 3159424, 145529893, 8737971990, 664337673319, 62461188300465, 7121505696653881, 968606284138975286, 154985833403909522361, 28828521246104115576631, 6169483384435711859804021, 1505386674395483103372685258, 415493606617772745031305469471
Offset: 0
-
terms = 19; A[] = 0; Do[A[x] = 1/((1-x)*(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)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+sum(k=1, 2, stirling(2, 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
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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;
A385759
G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^4*A'''(x))).
Original entry on oeis.org
1, 2, 5, 15, 141, 3932, 251717, 31216948, 6680698525, 2271470142438, 1153913665217481, 835435792656039975, 830424340158140342961, 1099482665756962845820704, 1891111018270919721409143729, 4137752010118540256190073466415, 11312615890237585633045672755792789
Offset: 0
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terms = 17; A[] = 0; Do[A[x] = 1/((1-x)*(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)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+sum(k=1, 3, stirling(3, k, 1)*j^k))*v[j+1]*v[i-j])); v;
A385760
G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^5*A''''(x))).
Original entry on oeis.org
1, 2, 5, 15, 51, 1412, 175067, 63725638, 53784616915, 90573359145678, 274256185472187231, 1383348290257488337035, 10961652126528967555229301, 130268275255842369871718355444, 2235924687457083597476492688851325, 53724798520519979444347750309693062183
Offset: 0
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terms = 16; A[] = 0; Do[A[x] = 1/((1-x)*(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)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+sum(k=1, 4, stirling(4, k, 1)*j^k))*v[j+1]*v[i-j])); v;
A385838
a(n) = 1 + Sum_{k=0..n-1} (1 + k^5) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 2, 7, 247, 61006, 62715298, 196236522104, 1526720482525833, 25665699044532909262, 841116296816234980686001, 49670440804927429155777517363, 4967242766473223753247263215133503, 799999284003076533259467892632499306811, 199068621859048073152067295737349123675521467
Offset: 0
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a_vector(n) = my(v=vector(n+1)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+j^5)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.