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URL: https://oeis.org/A244821

⇱ A244821 - OEIS

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A244821
E.g.f.: Sum_{n>=0} exp(n*3^n*x) * x^n/n!.
4
1, 1, 7, 82, 2377, 125956, 13786849, 2767780450, 1068587690545, 755247058160104, 990216775791709921, 2368086973433913986398, 10296184143094869761471305, 81305381330548263178299374860, 1153396004725120797831718629888193, 29585981132637810261211357828811890786
OFFSET
0,3
FORMULA
O.g.f.: Sum_{n>=0} x^n/(1 - n*3^n*x)^(n+1).
a(n) = Sum_{k=0..n} C(n,k) * k^(n-k) * 3^(k*(n-k)).
EXAMPLE
E.g.f.: A(x) = 1 + x + 7*x^2/2! + 82*x^3/3! + 2377*x^4/4! + 125956*x^5/5! +...
where
A(x) = 1 + exp(3*x)*x + exp(3^2*x)^2*x^2/2! + exp(3^3*x)^3*x^3/3! + exp(3^4*x)^4*x^4/4! + exp(3^5*x)^5*x^5/5! + exp(3^6*x)^6*x^6/6! +...
MAPLE
N:= 31:
S:= series(add(exp(n*3^n*x)*x^n/n!, n=0..N), x, N):
seq(coeff(S, x, j)*j!, j=0..N-1); # Robert Israel, Jul 04 2017
MATHEMATICA
Flatten[{1, Table[Sum[Binomial[n, k]*k^(n-k)*3^(k*(n-k)), {k, 0, n}], {n, 1, 20}]}] (* Vaclav Kotesovec, Jul 11 2014 *)
PROG
(PARI) a(n) = sum(k=0, n, binomial(n, k) * k^(n-k) * 3^(k*(n-k)) )
for(n=0, 25, print1(a(n), ", "))
(PARI) a(n)=n!*polcoeff(sum(k=0, n, exp(k*3^k*x +x*O(x^n))*x^k/k!), n)
for(n=0, 25, print1(a(n), ", "))
(PARI) a(n)=polcoeff(sum(k=0, n, x^k/(1-k*3^k*x +x*O(x^n))^(k+1)), n)
for(n=0, 25, print1(a(n), ", "))
CROSSREFS
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Jul 06 2014
STATUS
approved