A326423 G.f. A(x) satisfies: Sum_{n>=0} A(x)^(n*(n+1)/2) * x^n = Sum_{n>=0} x^n / (1-x)^(n*(n-1)/2).

1, 0, 1, 1, 4, 11, 39, 147, 598, 2577, 11669, 55156, 270938, 1378577, 7247494, 39290662, 219304105, 1258592815, 7418414658, 44863100701, 278117328554, 1765909629266, 11475651209600, 76267987517000, 518046275820877, 3593989140928928, 25450794447346211, 183860936257142088, 1354254148649619126, 10164913983190913353, 77710718331267769117

Offset: 0

Author

Paul D. Hanna, Jul 03 2019

Keywords

• nonn

Examples

			G.f.: A(x) = 1 + x^2 + x^3 + 4*x^4 + 11*x^5 + 39*x^6 + 147*x^7 + 598*x^8 + 2577*x^9 + 11669*x^10 + 55156*x^11 + 270938*x^12 + 1378577*x^13 + 7247494*x^14 + ...
such that the following series are equal
B(x) = 1 + A(x)*x + A(x)^3*x^2 + A(x)^6*x^3 + A(x)^10*x^4 + A(x)^15*x^5 + A(x)^21*x^6 + A(x)^28*x^7 + A(x)^36*x^8 + A(x)^45*x^9 + ...
and
B(x) = 1 + x + x^2/(1-x) + x^3/(1-x)^3 + x^4/(1-x)^6 + x^5/(1-x)^10 + x^6/(1-x)^15 + x^7/(1-x)^21 + x^8/(1-x)^28 + x^9/(1-x)^36 + ...
where
B(x) = 1 + x + x^2 + 2*x^3 + 5*x^4 + 14*x^5 + 43*x^6 + 143*x^7 + 510*x^8 + 1936*x^9 + 7775*x^10 + 32869*x^11 + 145665*x^12 + ... + A098569(n-1)*x^n + ...
		

Links

• Paul D. Hanna, Table of n, a(n) for n = 0..300

Crossrefs

Cf. A098569, A326424, A325294.

Programs

PARI

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