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;
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;
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;
A385836
a(n) = 1 + Sum_{k=0..n-1} (1 + k^3) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 2, 7, 79, 2446, 166618, 21508712, 4732995201, 1642479584974, 847546182102241, 621260202463120771, 623749689526374747439, 832709044623310548285995, 1442255257225526024262579955, 3174408056872712362090099214740, 8723280646832436679639469748539639
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^3)*v[j+1]*v[i-j])); v;
A385845
G.f. A(x) satisfies A(x) = 1/((1 - x) * (1 - x^4*A'''(x))).
Original entry on oeis.org
1, 1, 1, 1, 7, 175, 10675, 1291675, 272543461, 91847148373, 46382810082589, 33442006088446669, 33141028037446336195, 43779298038683546954491, 75169054733013247990186039, 164244384592052866115015051119, 448551414321306169623754824645385
Offset: 0
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terms = 17; A[] = 0; Do[A[x] = 1/((1 - x) * (1 - x^4*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, 3, stirling(3, k, 1)*j^k)*v[j+1]*v[i-j])); v;
Showing 1-5 of 5 results.