A298690 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, 2, 10, 83, 971, 14679, 271065, 5887674, 146573343, 4106195739, 127709962780, 4364136955874, 162503129082497, 6548680061635319, 283973223632787150, 13185195626147207058, 652695122347799336199, 34316223642036784123819, 1909798106976656110119169, 112165977515060359849066878, 6933265352057611483132200642

Offset

0,3

Links

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

Example

G.f.: A(x) = 1 + x + 2*x^2 + 10*x^3 + 83*x^4 + 971*x^5 + 14679*x^6 + 271065*x^7 + 5887674*x^8 + 146573343*x^9 + 4106195739*x^10 + 127709962780*x^11 + 4364136955874*x^12 + 162503129082497*x^13 + 6548680061635319*x^14 + 283973223632787150*x^15 + ...
such that
A(x) = 1 + C(1,1)*x/A(x) + C(3,2)*x^2/A(x)^3 + C(6,3)*x^3/A(x)^6 + C(10,4)*x^4/A(x)^10 + C(15,5)*x^5/A(x)^15 + C(21,6)*x^6/A(x)^21 + C(28,7)*x^7/A(x)^28 + ...
more explicitly,
A(x) = 1 + x/A(x) + 3*x^2/A(x)^3 + 20*x^3/A(x)^6 + 210*x^4/A(x)^10 + 3003*x^5/A(x)^15 + 54264*x^6/A(x)^21 + 1184040*x^7/A(x)^28 + 30260340*x^8/A(x)^36 + ...

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) ))); G=Ser(A); A[n+1]}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A014068, A298689, A298691.

Sequence in context: A003093 A006679 A050390 * A101878 A121194 A302572

Adjacent sequences: A298687 A298688 A298689 * A298691 A298692 A298693

Keyword

nonn

Author

Paul D. Hanna, Jan 24 2018

Status

approved