login

Year-end appeal: Please make a donation to the OEIS Foundation to support ongoing development and maintenance of the OEIS. We are now in our 61st year, we have over 378,000 sequences, and we’ve reached 11,000 citations (which often say “discovered thanks to the OEIS”).

A095793
G.f.: A(x) = 1+x*(1+x*(1+x*(...(1+x*(...)^n)...)^3)^2)^1.
14
1, 1, 1, 2, 7, 36, 245, 2072, 20913, 245012, 3265581, 48766020, 806254126, 14616629622, 288272307999, 6144034279588, 140715744051270, 3446290524236454, 89874216926157157, 2486386071747194244
OFFSET
0,4
LINKS
Vaclav Kotesovec, Table of n, a(n) for n = 0..350 (terms 0..200 from Paul D. Hanna)
EXAMPLE
G.f.: 1 + x + x^2 + 2*x^3 + 7*x^4 + 36*x^5 + 245*x^6 + 2072*x^7 +...
such that
A(x) = 1 + x*B(x), B(x) = 1 + x*C(x)^2, C(x) = 1 + x*D(x)^3, D(x) = 1 + x*E(x)^4, E(x) = 1 + x*F(x)^5, F(x) = 1 + x*G(x)^6, G(x) = 1 + x*H(x)^7, ...
where A(x), B(x), C(x), ... are the g.f. of the sequences given below.
A: [1, 1, 1, 2, 7, 36, 245, 2072, 20913, 245012, ...];
B: [1, 1, 2, 7, 36, 245, 2072, 20913, 245012, 3265581, ...];
C: [1, 1, 3, 15, 103, 888, 9147, 109150, 1477575, 22349316, ...];
D: [1, 1, 4, 26, 224, 2351, 28760, 399314, 6183132, 105455687, ...];
E: [1, 1, 5, 40, 415, 5145, 73121, 1162620, 20358145, 388334030, ...];
F: [1, 1, 6, 57, 692, 9906, 160656, 2884554, 56502264, 1195386975, ...];
G: [1, 1, 7, 77, 1071, 17395, 317303, 6357267, 137950303, 3211604480, ...];
H: [1, 1, 8, 100, 1568, 28498, 577808, 12788776, 304827080, 7753676623, ...];
I: [1, 1, 9, 126, 2199, 44226, 987021, 23928972, 621887265, 17173176273, ...]; ...
FIRST DERIVATIVES OF SERIES:
A' = B + x*C^2 + 2!*x^2*C*D^3 + 3!*x^3*C*D^2*E^4 + 4!*x^4*C*D^2*E^3*F^5 + 5!*x^5*C*D^2*E^3*F^4*G^6 + 6!*x^6*C*D^2*E^3*F^4*G^5*H^7 +...
B' = C^2 + 2!*x*C*D^3 + 3!*x^2*C*D^2*E^4 + 4!*x^3*C*D^2*E^3*F^5 + 5!*x^4*C*D^2*E^3*F^4*G^6 + 6!*x^5*C*D^2*E^3*F^4*G^5*H^7 +...
2!*C' = 2!*D^3 + 3!*x*D^2*E^4 + 4!*x^2*D^2*E^3*F^5 + 5!*x^3*D^2*E^3*F^4*G^6 + 6!*x^4*D^2*E^3*F^4*G^5*H^7 + 7!*x^5*D^2*E^3*F^4*G^5*H^6*I^8 +...
PROG
(PARI) {a(n)=local(A); A=1+x+x*O(x^n); for(j=0, n-1, A=1+x*A^(n-j)); polcoeff(A, n)}
for(n=0, 20, print1(a(n), ", "))
(PARI) /* Print Row r in Table (this Sequence is at r=1) */
{a(n, r=1)=local(A=vector(3*n+2*r+2, i, 1+x));
for(m=1, 2*n+r, for(j=0, n+r+m, A[n+r+m-j+1]=1+x*(A[n+r+m-j+2] +x^r*O(x^n))^(n+r+m-j+1) ); ); polcoeff(A[r], n)}
for(n=0, 20, print1(a(n, 1), ", "))
CROSSREFS
Sequence in context: A201197 A185754 A191493 * A029768 A180271 A380081
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jun 06 2004
STATUS
approved