A325581 G.f.: Sum_{n>=0} (n+1) * x^n * (1+x)^(n*(n+1)).

1, 2, 7, 24, 98, 430, 2062, 10610, 58240, 338984, 2081189, 13423258, 90626012, 638509008, 4682120763, 35650040782, 281266115870, 2295142774336, 19338107378888, 167987656339604, 1502475101768767, 13818574571596432, 130542011977462175, 1265358001625542030, 12572822521590475349, 127943980062492526520, 1332336499429857507073, 14186629118985647254622, 154348478009342665050329, 1714707987491310848285920

Offset

0,2

Comments

Equals column 1 of triangle A325580.

Links

Table of n, a(n) for n=0..29.

Example

G.f.: A(x) = 1 + 2*x + 7*x^2 + 24*x^3 + 98*x^4 + 430*x^5 + 2062*x^6 + 10610*x^7 + 58240*x^8 + 338984*x^9 + 2081189*x^10 + 13423258*x^11 + 90626012*x^12 + ...
such that
A(x) = 1 + 2*x*(1+x)^2 + 3*x^2*(1+x)^6 + 4*x^3*(1+x)^12 + 5*x^4*(1+x)^20 + 6*x^5*(1+x)^30 + 7*x^6*(1+x)^42 + 8*x^7*(1+x)^(56) + 9*x^8*(1+x)^72 + ...

Prog

(PARI) {a(n) = my(A = sum(m=0, n, (m+1) * x^m * (1+x +x*O(x^n))^(m*(m+1)) )); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A325580, A121689, A325586, A325587.

Sequence in context: A150432 A150433 A197554 * A162044 A150434 A150435

Adjacent sequences: A325578 A325579 A325580 * A325582 A325583 A325584

Keyword

nonn

Author

Paul D. Hanna, May 11 2019

Status

approved