A144003 -id:A144003 - cp's OEIS frontend

A144002 E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral 1/A(x)^2 dx ).

1, 1, 2, 10, 88, 1152, 20448, 464608, 12998176, 435443328, 17106187520, 775347933312, 40025403691136, 2328514989726720, 151324140857050624, 10904257049278844416, 865717992565002800640, 75309304802558209263616, 7143418423952431605493760, 735668180680897524348745728

Offset: 0

Paul D. Hanna, Sep 07 2008

nonn

			E.g.f.: A(x) = 1 + x + 2*x^2/2! + 10*x^3/3! + 88*x^4/4! + 1152*x^5/5! + ...

Paul D. Hanna, Table of n, a(n) for n = 0..100

Cf. A001028, A144003, A144004.

{a(n) = my(A=1+x+x*O(x^n)); for(i=0,n, A = 1 + serreverse(intformal(1/A^2))); n!*polcoef(A,n)}
for(n=0,20,print1(a(n),", "))

E.g.f. A(x) satisfies: A'(x) = A(A(x) - 1)^2. - Paul D. Hanna, Nov 25 2014 [corrected by Paul D. Hanna, Sep 07 2024]

A144004 E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral 1/A(x)^4 dx ).

Original entry on oeis.org

1, 1, 4, 44, 856, 24664, 958592, 47463936, 2881313024, 208638075392, 17654019768320, 1717961286944768, 189836122499649536, 23574107397852049408, 3261667682403085852672, 499151625979680748978176

Offset: 0

Paul D. Hanna, Sep 07 2008

nonn

			E.g.f.: A(x) = 1 + x + 4*x^2/2! + 44*x^3/3! + 856*x^4/4! + 24664*x^5/5! + 958592*x^6/6! + 47463936*x^7/7! + 2881313024*x^8/8! + ...

Cf. A001028, A144002, A144003.

{a(n) = my(A=1+x+x*O(x^n)); for(i=0,n, A = 1 + serreverse(intformal(1/A^4))); n!*polcoef(A,n)}
for(n=0,20,print1(a(n),", "))

E.g.f. A(x) satisfies: A'(x) = A(A(x) - 1)^4. - Paul D. Hanna, Sep 07 2024

cp's OEIS Frontend

A144002 E.g.f. A(x) satisfies: A(x) = 1 + Series_Reversion( Integral 1/A(x)^2 dx ).

Views

Author

Keywords

Examples

Links

Crossrefs

Programs

PARI

Formula