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;
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;
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;
A385832
a(0) = 1; a(n) = Sum_{k=0..n-1} (1 + k^4) * a(k) * a(n-1-k).
Original entry on oeis.org
1, 1, 3, 56, 4705, 1218747, 765389596, 994245193386, 2390167881074445, 9797301213263859467, 64309492440202351088387, 643287882516349276270085850, 9420307945482704895570131173916, 195367768417628005309741727943311572, 5580484965405704420901774303244279908840
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^4)*v[j+1]*v[i-j])); v;
A385922
E.g.f. A(x) satisfies A(x) = exp(x*A(x) + x^5*A''''(x)).
Original entry on oeis.org
1, 1, 3, 16, 125, 16296, 11929927, 30230776864, 203634850471929, 3082625458810336000, 93280255561776693446891, 5173509703646410927969711104, 491814532626655136406839912703157, 75968624000349445912469318939348786176, 18252829396078618393615717880609268502659375
Offset: 0
-
terms = 15; A[] = 1; Do[A[x] = Exp[x*A[x]+x^5*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, 4, stirling(4, k, 1)*j^k))*binomial(i-1, j)*v[j+1]*v[i-j])); v;
A386450
G.f. A(x) satisfies A(x) = 1/(1 - x - x^5*A''''(x)).
Original entry on oeis.org
1, 1, 1, 1, 1, 25, 3049, 1103713, 929323297, 1563120681841, 4730002253928145, 23848669801185169825, 188929157434986723256801, 2244856224793842495701519113, 38526222340982767558002054899641, 925631015719595748793089592291450945, 30325523298479173582153602405524578371265
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, 4, stirling(4, k, 1)*j^k)*v[j+1]*v[i-j])); v;
Showing 1-6 of 6 results.