A325298 G.f. A(x) satisfies: Sum_{n>=0} x^(n*(n+1)/2) * A(x)^n = Sum_{n>=0} x^n * (1+x)^(n*(n+1)/2).

1, 2, 3, 6, 17, 56, 189, 673, 2561, 10321, 43612, 192439, 884702, 4227202, 20942697, 107363291, 568547892, 3105231155, 17467413871, 101069173004, 600841031279, 3665958252167, 22933712331957, 146968161483626, 963973640814332, 6466300466801210, 44327544752355141, 310325239786656220, 2217191324979383686, 16157187739844358535, 120020165206009363396, 908305634422244782653, 6999639387956913535113

Offset

0,2

Links

Table of n, a(n) for n=0..32.

Example

G.f.: A(x) = 1 + 2*x + 3*x^2 + 6*x^3 + 17*x^4 + 56*x^5 + 189*x^6 + 673*x^7 + 2561*x^8 + 10321*x^9 + 43612*x^10 + 192439*x^11 + 884702*x^12 + ...
such that the following series are equal
B(x) = 1 + x*A(x) + x^3*A(x)^2 + x^6*A(x)^3 + x^10*A(x)^4 + x^15*A(x)^5 + x^21*A(x)^6 + x^28*A(x)^7 + x^36*A(x)^8 + x^45*A(x)^9 + ...
B(x) = 1 + x*(1+x) + x^2*(1+x)^3 + x^3*(1+x)^6 + x^4*(1+x)^10 + x^5*(1+x)^15 + x^6*(1+x)^21 + x^7*(1+x)^28 + x^8(1+x)^36 + x^9*(1+x)^45 + ...
where
B(x) = 1 + x + 2*x^2 + 4*x^3 + 10*x^4 + 27*x^5 + 81*x^6 + 262*x^7 + 910*x^8 + 3363*x^9 + 13150*x^10 + 54135*x^11 + 233671*x^12 + ... + A121690(n)*x^n + ...

Prog

(PARI) {a(n) = my(A=[1]); for(i=1, n, A=concat(A, 0);
A[#A] = -polcoeff( sum(m=0, #A, x^(m*(m+1)/2)*Ser(A)^m - x^m*(1+x +x*O(x^#A) )^(m*(m+1)/2) ), #A) ); A[n+1]}
for(n=0, 35, print1(a(n), ", "))

Crossrefs

Cf. A121690.

Sequence in context: A078344 A024498 A319283 * A361380 A073591 A114491

Adjacent sequences: A325295 A325296 A325297 * A325299 A325300 A325301

Keyword

nonn

Author

Paul D. Hanna, Apr 28 2019

Status

approved