A325047 Odd coefficients in Sum_{n>=0} x^n * (1 + x^n)^n / (1 - x^(n+1))^(n+1).

1, 3, 9, 27, 99, 657, 4109, 14423, 53475, 134523, 1686983, 13421711, 85848955, 325004679, 1482972731, 6258674687, 43509358107, 310036393025, 1197637196163, 5063711906615, 29684695980709, 237651736873787, 1908882337833375, 13472425062258959, 63600578042733379, 259398342483031449, 854224450257439461, 3641411522409674437, 30995855770329029579, 177818838160621615805, 864729932377687089877, 6784148623461403996159

Offset

0,2

Comments

a(n) = A325046(n*(n+1)) for n >= 0.

Links

Paul D. Hanna, Table of n, a(n) for n = 0..100

Formula

a(n) = [x^(n*(n+1))] Sum_{k>=0} x^k * (1 + x^k)^k / (1 - x^(k+1))^(k+1).

a(n) = [x^(n*(n+1))] Sum_{m>=0} x^m * Sum_{k=0..m} binomial(m,k) * (x^m + x^k)^(m-k).

a(n) = [x^(n*(n+1))] Sum_{m>=0} x^m * Sum_{k=0..m} binomial(m,k) * Sum_{j=0..m-k} binomial(m-k,j) * x^((m-k)*(m-j)).

Prog

(PARI) {A325046(n) = my(A=sum(m=0, n, x^m * (1 + x^m +x*O(x^n))^m/(1 - x^(m+1) +x*O(x^n))^(m+1) )); polcoeff(A, n)}
for(n=0, 30, print1(A325046(n*(n+1)), ", "))

Crossrefs

Cf. A325046, A323679 (variant).

Sequence in context: A148927 A148928 A029527 * A148929 A148930 A230951

Adjacent sequences: A325044 A325045 A325046 * A325048 A325049 A325050

Keyword

nonn

Author

Paul D. Hanna, Mar 26 2019

Status

approved