A298691 G.f. A(x) satisfies: A(x) = Sum_{n>=0} binomial( n*(n+1)/2, n) * x^n / A(x)^( n*(n-1)/2 ).

1, 1, 3, 17, 144, 1647, 24037, 429483, 9088749, 221942779, 6130801041, 188708846991, 6398116247554, 236786117903526, 9495515095867953, 410104221125229354, 18977504682428845671, 936731766873748776822, 49127713187418767376060, 2728178479576867266738579, 159924801506251429348644138, 9868564065320443974954599471

Offset

0,3

Links

Table of n, a(n) for n=0..21.

Example

G.f.: A(x) = 1 + x + 3*x^2 + 17*x^3 + 144*x^4 + 1647*x^5 + 24037*x^6 + 429483*x^7 + 9088749*x^8 + 221942779*x^9 + 6130801041*x^10 + 188708846991*x^11 + 6398116247554*x^12 + 236786117903526*x^13 + 9495515095867953*x^14 + 410104221125229354*x^15 + ...
such that
A(x) = 1 + C(1,1)*x + C(3,2)*x^2/A(x) + C(6,3)*x^3/A(x)^3 + C(10,4)*x^4/A(x)^6 + C(15,5)*x^5/A(x)^10 + C(21,6)*x^6/A(x)^15 + C(28,7)*x^7/A(x)^21 + ...
more explicitly,
A(x) = 1 + x + 3*x^2/A(x) + 20*x^3/A(x)^3 + 210*x^4/A(x)^6 + 3003*x^5/A(x)^10 + 54264*x^6/A(x)^15 + 1184040*x^7/A(x)^21 + 30260340*x^8/A(x)^28 + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A = Vec(sum(m=0, #A, binomial(m*(m+1)/2, m) * x^m/Ser(A)^(m*(m-1)/2) ))); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A014068, A298689, A298690.

Sequence in context: A268254 A333331 A198860 * A362282 A051442 A368236

Adjacent sequences: A298688 A298689 A298690 * A298692 A298693 A298694

Keyword

nonn

Author

Paul D. Hanna, Jan 24 2018

Status

approved