A301465 G.f.: Sum_{n>=0} ( (1+x)^n + (1+2*x)^n )^n * x^n.

1, 2, 7, 32, 180, 1142, 8162, 63807, 541202, 4926969, 47799429, 491254999, 5322191407, 60533874755, 720300053902, 8939841040157, 115427887156492, 1546880293065700, 21472465304481214, 308173758866549496, 4565492159926897329, 69713352146246150541, 1095715822838490323551, 17705238547423980566108, 293792275476690070452598

Offset

0,2

Links

Table of n, a(n) for n=0..24.

Formula

G.f.: Sum_{n>=0} x^n * Sum_{k=0..n} binomial(n,k) * (1+x)^(n*(n-k)) * (1+2*x)^(n*k).

Example

G.f.: A(x) = 1 + 2*x + 7*x^2 + 32*x^3 + 180*x^4 + 1142*x^5 + 8162*x^6 + 63807*x^7 + 541202*x^8 + 4926969*x^9 + 47799429*x^10 + ...
such that
A(x) = 1 + ((1+x) + (1+2*x))*x + ((1+x)^2 + (1+2*x)^2)^2*x^2 + ((1+x)^3 + (1+2*x)^3)^3*x^3 + ((1+x)^4 + (1+2*x)^4)^4*x^4 + ((1+x)^5 + (1+2*x)^5)^5*x^5 + ...

Prog

(PARI) {a(n) = my(A=1); A = sum(k=0, n, ((1+x)^k + (1+2*x)^k +x*O(x^n))^k * x^k ); polcoeff(A, n)}
for(n=0, 30, print1(a(n), ", "))

Crossrefs

Cf. A301306, A301312, A301308.

Sequence in context: A121555 A265165 A351813 * A097900 A198891 A000153

Adjacent sequences: A301462 A301463 A301464 * A301466 A301467 A301468

Keyword

nonn

Author

Paul D. Hanna, Mar 24 2018

Status

approved