OFFSET
1,2
COMMENTS
FORMULA
L.g.f.: L(x) = x + 9*x^2/2 + 40*x^3/3 + 245*x^4/4 + 756*x^5/5 + 5544*x^6/6 + 13728*x^7/7 + 96525*x^8/8 + 316030*x^9/9 + 1662804*x^10/10 + 4232592*x^11/11 + 37858184*x^12/12 + ... + a(n)*x^n/n + ...
equivalently,
L(x) = 1*1*x + 3*3*x^2/2 + 4*10*x^3/3 + 7*35*x^4/4 + 6*126*x^5/5 + 12*462*x^6/6 + 8*1716*x^7/7 + 15*6435*x^8/8 + ... + sigma(n)*binomial(2*n-1,n)*x^n/n + ...
where exponentiation yields the integer series given by A156305:
exp(L(x)) = 1 + x + 5*x^2 + 18*x^3 + 87*x^4 + 290*x^5 + 1553*x^6 + 5015*x^7 + 25436*x^8 + 94500*x^9 + 431464*x^10 + ... + A156305(n)*x^n + ...
PROG
(PARI) {a(n) = sigma(n) * binomial(2*n-1, n)}
for(n=1, 30, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Nov 14 2022
STATUS
approved