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
Keywords
Examples
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,...].
Programs
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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)))}
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