A190633 G.f. satisfies: A(x) = 1 + x*A(x*A(x*A(x*A(x*...x*A(x*...)^n...)^4)^3)^2)^1.

1, 1, 1, 3, 16, 118, 1077, 11486, 138444, 1847148, 26912226, 424290217, 7194012328, 130641675418, 2534008088656, 52404312807800, 1154031769467768, 27034986095711172, 673063391032594741, 17786452294614118713, 498174223396072711297, 14762117810503938465521, 461836676823537625928868

Offset

0,4

Links

Vaclav Kotesovec, Table of n, a(n) for n = 0..150

Example

G.f.: A(x) = 1 + x + x^2 + 3*x^3 + 16*x^4 + 118*x^5 + 1077*x^6 + 11486*x^7 +...
where
A(x) = 1 + x*A(x*B(x)^2)
B(x) = A(x*C(x)^3) = 1 + x + 4*x^2 + 27*x^3 + 242*x^4 + 2613*x^5 +...
C(x) = A(x*D(x)^4) = 1 + x + 5*x^2 + 41*x^3 + 436*x^4 + 5493*x^5 +...
D(x) = A(x*E(x)^5) = 1 + x + 6*x^2 + 58*x^3 + 716*x^4 + 10353*x^5 +...
E(x) = A(x*F(x)^6) = 1 + x + 7*x^2 + 78*x^3 + 1098*x^4 + 17954*x^5 +...
F(x) = A(x*G(x)^7) = 1 + x + 8*x^2 + 101*x^3 + 1598*x^4 + 29182*x^5 +...
...
The coefficients in the functions A_{n}(x) = A(x*A_{n+1}(x)^(n+1)) begin:
n=1: [1, 1, 3, 16, 118, 1077, 11486, 138444, 1847148, ...];
n=2: [1, 1, 4, 27, 242, 2613, 32361, 446981, 6767752, ...];
n=3: [1, 1, 5, 41, 436, 5493, 78411, 1236675, 21220924, ...];
n=4: [1, 1, 6, 58, 716, 10353, 168128, 2995118, 57697373, ...];
n=5: [1, 1, 7, 78, 1098, 17954, 327516, 6516816, 139510116, ...];
n=6: [1, 1, 8, 101, 1598, 29182, 591387, 13012390, 306746446, ...];
n=7: [1, 1, 9, 127, 2232, 45048, 1004657, 24234584, 624104908, ...];
n=8: [1, 1, 10, 156, 3016, 66688, 1623642, 42621080, 1190879427, ...];
n=9: [1, 1, 11, 188, 3966, 95363, 2517354, 71454120, 2153352732, ...];
n=10:[1, 1, 12, 223, 5098, 132459, 3768797, 115036935, 3719861220,...];
n=11:[1, 1, 13, 261, 6428, 179487, 5476263, 178886981, 6178793404,...];
n=12:[1, 1, 14, 302, 7972, 238083, 7754628, 269945982, 9919784089,...];
n=13:[1, 1, 15, 346, 9746, 310008, 10736648, 396806780, 15458366420,...];
n=14:[1, 1, 16, 393, 11766, 397148, 14574255, 569956992, 23464343946,...];
n=15:[1, 1, 17, 443, 14048, 501514, 19439853, 802039474, 34794144844,...];
...
The coefficients in the functions A_{n}(x)^n = A(x*A_{n+1}(x)^(n+1))^n begin:
n=1: [1, 1, 3, 16, 118, 1077, 11486, 138444, 1847148, ...];
n=2: [1, 2, 9, 62, 554, 5926, 72613, 992656, 14888020, ...];
n=3: [1, 3, 18, 154, 1644, 20523, 288977, 4490214, ...];
n=4: [1, 4, 30, 308, 3849, 55332, 886740, 15542428, ...];
n=5: [1, 5, 45, 540, 7755, 126601, 2283415, 44720260, ...];
n=6: [1, 6, 63, 866, 14073, 257658, 5175458, 112225428, ...];
n=7: [1, 7, 84, 1302, 23639, 480207, 10642667, 253418838, ...];
n=8: [1, 8, 108, 1864, 37414, 835624, 20269388, 526168488, ...];
n=9: [1, 9, 135, 2568, 56484, 1376253, 36282528, 1020278988, ...];
n=10:[1, 10, 165, 3430, 82060, 2166702, 61706375, 1869264840, ...];
n=11:[1, 11, 198, 4466, 115478, 3285139, 100534225, 3264729622, ...];
n=12:[1, 12, 234, 5692, 158199, 4824588, 157916816, 5473613220, ...];
n=13:[1, 13, 273, 7124, 211809, 6894225, 240367569, 8858569252, ...];
n=14:[1, 14, 315, 8778, 278019, 9620674, 355984636, 13901734828, ...];
n=15:[1, 15, 360, 10670, 358665, 13149303, 514689755, 21232154790, ...];
...

Prog

(PARI) {a(n)=local(A, G=1+x); for(j=0, n, A=1+x*G; for(i=0, n-1, G=subst(A, x, x*(G+x*O(x^n))^(n-i+1)))); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Sequence in context: A221409 A074522 A302701 * A220352 A333682 A125807

Adjacent sequences: A190630 A190631 A190632 * A190634 A190635 A190636

Keyword

nonn

Author

Paul D. Hanna, Mar 02 2013

Status

approved