A156360 G.f.: A(x) = exp( Sum_{n>=1} sigma_n(2n)*x^n/n ), where sigma_n(2n) is the sum of the n-th powers of the divisors of 2*n.

1, 3, 15, 120, 1450, 25383, 591563, 17156364, 595635903, 24023004840, 1102221504614, 56652798990909, 3222918574782830, 200989079661549750, 13632214370613131094, 998992560620311541814, 78653794343072884416393

Offset

0,2

Links

Table of n, a(n) for n=0..16.

Formula

a(n) = (1/n)*Sum_{k=1..n} sigma(2*k,k)*a(n-k) for n>0, with a(0) = 1.

a(n) ~ 2^n * n^(n-1). - Vaclav Kotesovec, Oct 31 2024

Example

G.f.: A(x) = 1 + 3*x + 15*x^2 + 120*x^3 + 1450*x^4 + 25383*x^5 +...
log(A(x)) = 3*x + 21*x^2/2 + 252*x^3/3 + 4369*x^4/4 + 103158*x^5/5 +...
sigma(2n,n) = [3,21,252,4369,103158,3037530,106237176,4311810305,...].

Prog

(PARI) {a(n)=polcoeff(exp(sum(k=1, n, sigma(2*k, k)*x^k/k, x*O(x^n))), n)}
(PARI) {a(n)=if(n==0, 1, (1/n)*sum(k=1, n, sigma(2*k, k)*a(n-k)))}

Crossrefs

Cf. variant: A023881 (number of partitions in expanding space).

Cf. A179504.

Sequence in context: A093571 A093570 A107869 * A377105 A160884 A173468

Adjacent sequences: A156357 A156358 A156359 * A156361 A156362 A156363

Keyword

nonn

Author

Paul D. Hanna, Feb 08 2009

Status

approved