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
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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;
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;
A385761
G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x*A(x) - x^6*A'''''(x))).
Original entry on oeis.org
1, 2, 5, 15, 51, 188, 23291, 16862710, 42561503035, 286183563337662, 4328240254531111671, 130903298544350358627387, 7257802488822060515691899445, 689810579878520205782663179307100, 106537105206016369903910237449838232525, 25594900303804029125790200935921438169789415
Offset: 0
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terms = 16; A[] = 0; Do[A[x] = 1/((1-x)*(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)); for(i=0, n, v[i+1]=1+sum(j=0, i-1, (1+sum(k=1, 5, stirling(5, k, 1)*j^k))*v[j+1]*v[i-j])); v;
A385837
a(n) = 1 + Sum_{k=0..n-1} (1 + k^4) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 2, 7, 135, 11472, 2983290, 1876558882, 2439543938823, 5867113337771476, 24055177364999767957, 157922269330003687462469, 1579854504025376907525660119, 23136970006572094830720177877037, 479860765871358769352536441406761329, 13707222893156109310485886790873337444816
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^4)*v[j+1]*v[i-j])); v;
A385846
G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^5*A''''(x))).
Original entry on oeis.org
1, 1, 1, 1, 1, 25, 3025, 1092025, 918393025, 1543818675025, 4670051491951201, 23541729570926148241, 186474039931306081488961, 2215498068423847604734793641, 38020162352221648825602734209201, 913434400512125113270449340963296649, 29925024395177730837015182640209851847809
Offset: 0
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terms = 17; A[] = 0; Do[A[x] = 1/((1 - x) * (1 - x^5*A''''[x])) + O[x]^terms // Normal, terms]; CoefficientList[A[x], x] (* Stefano Spezia, Jul 10 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, sum(k=1, 4, stirling(4, k, 1)*j^k)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.