A292809 G.f. A(x) satisfies: A( 2*x - A(x) ) = 2*x - A(x) + x^2.

1, 1, 2, 9, 56, 420, 3572, 33328, 334354, 3559310, 39838760, 465743720, 5658983108, 71191948512, 924554859776, 12365546196641, 169995491295312, 2398380272232272, 34680290150700800, 513390937937217088, 7773229533145403728, 120277760289804227632, 1900583166564027019136, 30649888151334972466392, 504153517331248726221392, 8454018409655883681321232, 144451967918022160558965408, 2513925490162481746629200624, 44542176917098830784415314624

Offset: 1

Author

Paul D. Hanna, Sep 24 2017

Keywords

• nonn

Comments

Apart from signs, essentially the same as A138740.

Apparently a(n) = A276370(n) wherever defined. - R. J. Mathar, Sep 26 2017

Examples

			G.f.: A(x) = x + x^2 + 2*x^3 + 9*x^4 + 56*x^5 + 420*x^6 + 3572*x^7 + 33328*x^8 + 334354*x^9 + 3559310*x^10 + 39838760*x^11 + 465743720*x^12 + 5658983108*x^13 + 71191948512*x^14 + 924554859776*x^15 + 12365546196641*x^16 +...
such that A( 2*x - A(x) ) = 2*x - A(x) + x^2.
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 1..300

Crossrefs

Cf. A138740, A276370, A292810.

Programs

PARI

{a(n) = my(A=x, V=[1, 1]); for(i=1, n, V = concat(V, 0); A=x*Ser(V); V[#V] = Vec( subst(G=A, x, 2*x - A) )[#V]/(-1) ); V[n]}
for(n=1,30,print1(a(n),", "))