A242573 a(n) = [x^n] G(n-1,x) where G(n,x) is the n-th iteration of G(1,x) = x/(1-x+x^2), so that G(n,x) = G(n-1, G(1,x)) with G(0,x)=x.

1, 1, 2, 6, 24, 120, 702, 4445, 27812, 187911, 4154105, 226545132, 11811552612, 567839904255, 26530164469576, 1244353584654296, 59633342751369016, 2947881116272213508, 151083714566902161495, 8048911065786420441543, 446230730213409483222040

Offset

1,3

Links

Paul D. Hanna, Table of n, a(n) for n = 1..200

Example

Given x/(1-x+x^2) = x + x^2 - x^4 - x^5 + x^7 + x^8 - x^10 - x^11 + x^13 +...
form a table of coefficients in the iterations of x/(1-x+x^2) like so:
[1,  0,  0,   0,    0,     0,      0,       0,        0,        0, ...];
[1,  1,  0,  -1,   -1,     0,      1,       1,        0,       -1, ...];
[1,  2,  2,  -1,   -8,   -15,    -10,      22,       79,      112, ...];
[1,  3,  6,   6,  -11,   -73,   -201,    -309,       37,     1913, ...];
[1,  4, 12,  26,   24,  -116,   -808,   -3000,    -7566,    -9882, ...];
[1,  5, 20,  65,  155,   120,  -1379,  -10761,   -51202,  -183269, ...];
[1,  6, 30, 129,  464,  1225,    702,  -18978,  -169139,  -994138, ...];
[1,  7, 42, 224, 1057,  4235,  12411,    4445,  -301321, -3076795, ...];
[1,  8, 56, 356, 2064, 10752,  48000,  156416,    27812, -5458012, ...];
[1,  9, 72, 531, 3639, 23064, 132633,  658197,  2388060,   187911, ...];
[1, 10, 90, 755, 5960, 44265, 306742, 1942198, 10676571, 43159172, ...]; ...
then this sequence forms the main diagonal in the above table.

Prog

(PARI) {a(n)=local(A=x, G=x/(1-x+x^2)); for(i=1, n-1, A=subst(G, x, A+x*O(x^(n)))); polcoeff(A, n)}
for(n=1, 30, print1(a(n), ", "))

Crossrefs

Cf. A242574, A242575.

Sequence in context: A274970 A177525 A177532 * A223034 A177530 A324134

Adjacent sequences: A242570 A242571 A242572 * A242574 A242575 A242576

Keyword

nonn

Author

Paul D. Hanna, May 17 2014

Status

approved