A155804
E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n-1)/2).
Original entry on oeis.org
1, 1, 1, 4, 19, 161, 1606, 21022, 323485, 5874913, 122077756, 2871573596, 75437801539, 2193468714373, 70020045331510, 2437979768144026, 92073099488632441, 3753886179551636513, 164556499026975482008
Offset: 0
E.g.f.: A(x) = 1 + x + x^2/2! + 4*x^3/3! + 19*x^4/4! + 161*x^5/5! +...
where e.g.f. A(x) satisfies:
A(x) = 1 + x + x^2/2!*A(x) + x^3/3!*A(x)^3 + x^4/4!*A(x)^6 + x^5/5!*A(x)^10 +...
Let B(x) = A(x*B(x)) be the e.g.f. of A155805 then:
B(x) = 1 + x*B(x) + x^2/2!*B(x)^3 + x^3/3!*B(x)^6 + x^4/4!*B(x)^10 +...
B(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2656*x^5/5! + 47392*x^6/6! +...
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{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+sum(k=1,n,x^k*A^(k*(k-1)/2)/k!+x*O(x^n))); n!*polcoeff(A,n)}
A155805
E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n(n+1)/2).
Original entry on oeis.org
1, 1, 3, 19, 191, 2656, 47392, 1034335, 26721781, 798018616, 27058991246, 1027237384009, 43172232488959, 1990253576425960, 99871804451808040, 5419775866582473211, 316301430225674131433, 19756213549154356027408
Offset: 0
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 19*x^3/3! + 191*x^4/4! + 2656*x^5/5! +...
where e.g.f. A(x) satisfies:
A(x) = 1 + x*A(x) + x^2/2!*A(x)^3 + x^3/3!*A(x)^6 + x^4/4!*A(x)^10 +...
Let B(x) = A(x/B(x)) be the e.g.f. of A155804 then:
B(x) = 1 + x + x^2/2!*B(x) + x^3/3!*B(x)^3 + x^4/4!*B(x)^6 + x^5/5!*B(x)^10 +...
B(x) = 1 + x + x^2/2! + 4*x^3/3! + 19*x^4/4! + 161*x^5/5! + 1606*x^6/6! +...
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{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+sum(k=1,n,x^k*A^(k*(k+1)/2)/k!+x*O(x^n))); n!*polcoeff(A,n)}
A155806
E.g.f. satisfies: A(x) = Sum_{n>=0} x^n/n! * A(x)^(n^2).
Original entry on oeis.org
1, 1, 3, 22, 269, 4616, 102847, 2824816, 92355769, 3506278528, 151720849691, 7375146930944, 398113181435653, 23640909385071616, 1532325553233566743, 107698939845869111296, 8162300091585206125553, 663836705760309127184384
Offset: 0
E.g.f.: A(x) = 1 + x + 3*x^2/2! + 22*x^3/3! + 269*x^4/4! + 4616*x^5/5! +...
where e.g.f. A(x) satisfies:
A(x) = 1 + x*A(x) + x^2/2!*A(x)^4 + x^3/3!*A(x)^9 + x^4/4!*A(x)^16 +...
Let B(x) = A(x*B(x)) be the e.g.f. of A155807 then:
B(x) = 1 + x*B(x)^2 + x^2/2!*B(x)^6 + x^3/3!*B(x)^12 + x^4/4!*B(x)^20 +...
B(x) = 1 + x + 5*x^2/2! + 55*x^3/3! + 969*x^4/4! + 23661*x^5/5! + 741013*x^6/6! +...
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{a(n)=local(A=1+x+x*O(x^n));for(i=1,n,A=1+sum(k=1,n,x^k*A^(k^2)/k!+x*O(x^n))); n!*polcoeff(A,n)}
Showing 1-3 of 3 results.