A296231 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n / (1-x)^( n*(n+1) ) / A(x)^( (n+1)*(n+2)/2 ).

1, 1, 1, 2, 3, 7, 16, 48, 157, 586, 2362, 10214, 46672, 223752, 1118799, 5810185, 31237145, 173412537, 992006284, 5837461604, 35283954583, 218791917313, 1390314155401, 9044905749879, 60190822583318, 409404760891303, 2844213921090065, 20168470493811065, 145888129690256442, 1075859539461621404, 8084389249391405645, 61869341164985700882, 481984158600673224200

Offset

0,4

Links

Paul D. Hanna, Table of n, a(n) for n = 0..200

Example

G.f.: A(x) = 1 + x + x^2 + 2*x^3 + 3*x^4 + 7*x^5 + 16*x^6 + 48*x^7 + 157*x^8 + 586*x^9 + 2362*x^10 + 10214*x^11 + 46672*x^12 + 223752*x^13+ 1118799*x^14 + 5810185*x^15 + ...
such that
1 = 1/A(x) + x/(1-x)^2/A(x)^3 + x^2/(1-x)^6/A(x)^6 + x^3/(1-x)^12/A(x)^10 + x^4/(1-x)^20/A(x)^15 + x^5/(1-x)^30/A(x)^21 + x^6/(1-x)^42/A(x)^28 + x^7/(1-x)^56/A(x)^36 + ...

Prog

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

Crossrefs

Cf. A296230.

Sequence in context: A332885 A122031 A246829 * A089125 A289051 A282320

Adjacent sequences: A296228 A296229 A296230 * A296232 A296233 A296234

Keyword

nonn

Author

Paul D. Hanna, Jan 24 2018

Status

approved