A292809 - OEIS

%I #13 Sep 26 2017 11:16:11

%S 1,1,2,9,56,420,3572,33328,334354,3559310,39838760,465743720,

%T 5658983108,71191948512,924554859776,12365546196641,169995491295312,

%U 2398380272232272,34680290150700800,513390937937217088,7773229533145403728,120277760289804227632,1900583166564027019136,30649888151334972466392,504153517331248726221392,8454018409655883681321232,144451967918022160558965408,2513925490162481746629200624,44542176917098830784415314624

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

%C Apart from signs, essentially the same as A138740.

%C Apparently a(n) = A276370(n) wherever defined. - _R. J. Mathar_, Sep 26 2017

%H Paul D. Hanna, <a href="/A292809/b292809.txt">Table of n, a(n) for n = 1..300</a>

%e 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 +...

%e such that A( 2*x - A(x) ) = 2*x - A(x) + x^2.

%o (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]}

%o for(n=1,30,print1(a(n),", "))

%Y Cf. A138740, A276370, A292810.

%K nonn

%O 1,3

%A _Paul D. Hanna_, Sep 24 2017