A296230 G.f. A(x) satisfies: 1 = Sum_{n>=0} x^n / (1-x)^( n*(n+1)/2 ) / A(x)^( (n+1)*(n+2)/2 ).

1, 1, 0, 1, 0, 1, 1, 0, 4, 0, 6, 13, 9, 48, 101, 147, 542, 1244, 2385, 8158, 19191, 44960, 145355, 356921, 953648, 2971797, 7728368, 22395844, 68642687, 189610373, 577526057, 1770461983, 5170947386, 16264118299, 50488278032, 154687144811, 498055705248, 1577949582705, 5029555661992, 16520308729413, 53633742931559, 176588771399224

Offset

0,9

Links

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

Example

G.f.: A(x) = 1 + x + x^3 + x^5 + x^6 + 4*x^8 + 6*x^10 + 13*x^11 + 9*x^12 + 48*x^13 + 101*x^14 + 147*x^15 + 542*x^16 + 1244*x^17 + 2385*x^18 + 8158*x^19 + 19191*x^20 + ...
such that
1 = 1/A(x) + x/(1-x)/A(x)^3 + x^2/(1-x)^3/A(x)^6 + x^3/(1-x)^6/A(x)^10 + x^4/(1-x)^10/A(x)^15 + x^5/(1-x)^15/A(x)^21 + x^6/(1-x)^21/A(x)^28 + x^7/(1-x)^28/A(x)^36 + ...
Compare to the trivial identity:
1 = 1/(1+x) + x*(1+x)/(1+x)^3 + x^2*(1+x)^3/(1+x)^6 + x^3*(1+x)^6/(1+x)^10 + x^4*(1+x)^10/(1+x)^15 + x^5*(1+x)^15/(1+x)^21 + ...

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)/2)*x^n/Ser(A)^((n+1)*(n+2)/2)) ); A[#A]=V[#A] ); A[n+1]}
for(n=0, 40, print1(a(n), ", "))

Crossrefs

Cf. A296231.

Sequence in context: A262246 A194193 A265644 * A222889 A223114 A222832

Adjacent sequences: A296227 A296228 A296229 * A296231 A296232 A296233

Keyword

nonn

Author

Paul D. Hanna, Jan 24 2018

Status

approved