A326424 G.f. A(x) satisfies: Sum_{n>=0} A(x)^(n*(n+1)/2) * x^n = Sum_{n>=0} (1+x)^(n*(n-1)/2) * x^n.

1, 0, 1, 0, 3, 4, 20, 62, 251, 1002, 4295, 19086, 88369, 423957, 2104214, 10783054, 56969183, 309900293, 1733790827, 9965992962, 58801256594, 355808106682, 2206237014216, 14007443494601, 90994768741426, 604395083728629, 4101881493676885, 28426771732773415, 201044377117957190, 1450195412613951590, 10663346917944740350, 79885242459500736025

Offset

0,5

Links

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

Example

G.f.: A(x) = 1 + x^2 + 3*x^4 + 4*x^5 + 20*x^6 + 62*x^7 + 251*x^8 + 1002*x^9 + 4295*x^10 + 19086*x^11 + 88369*x^12 + 423957*x^13 + 2104214*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 + (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 + ...
where
B(x) = 1 + x + x^2 + 2*x^3 + 4*x^4 + 10*x^5 + 27*x^6 + 81*x^7 + 262*x^8 + 910*x^9 + 3363*x^10 + 13150*x^11 + 54135*x^12 + ... + A121690(n-1)*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*(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), ", "))

Crossrefs

Cf. A121690, A326423, A325289.

Sequence in context: A300499 A151419 A067281 * A151357 A250105 A009169

Adjacent sequences: A326421 A326422 A326423 * A326425 A326426 A326427

Keyword

nonn

Author

Paul D. Hanna, Jul 03 2019

Status

approved