A155201 G.f.: A(x) = exp( Sum_{n>=1} (2^n + 1)^n * x^n/n ), a power series in x with integer coefficients.

1, 3, 17, 285, 21747, 7894143, 12593691755, 84961748935779, 2379148487805445513, 273416748863491468927893, 128009274688933686165252807225, 242979449433397149030644307317592609, 1863847996727745781866688849374488247858333, 57652096246331953203644653244501049018464175026133

Offset

0,2

Comments

More generally, it appears that for m integer, exp( Sum_{n>=1} (m^n + y)^n * x^n/n ) is a power series in x and y with integer coefficients.

Links

Table of n, a(n) for n=0..13.

Formula

Equals row sums of triangle A155810.

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

a(n) = B_n( 0!*(2^1+1)^1, 1!*(2^2+1)^2, 2!*(2^3+1)^3, ..., (n-1)!*(2^n+1)^n ) / n!, where B_n() is the n-th complete Bell polynomial. - Max Alekseyev, Oct 10 2014

Example

G.f.: A(x) = 1 + 3*x + 17*x^2 + 285*x^3 + 21747*x^4 + 7894143*x^5 +...
log(A(x)) = 3*x + 5^2*x^2/2 + 9^3*x^3/3 + 17^4*x^4/4 + 33^5*x^5/5 +...

Prog

(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, (2^m+1)^m*x^m/m)+x*O(x^n)), n)}

Crossrefs

Cf. A155200, A155202, A155810 (triangle), variants: A155204, A155208.

Sequence in context: A153487 A267658 A365364 * A062622 A271609 A290806

Adjacent sequences: A155198 A155199 A155200 * A155202 A155203 A155204

Keyword

nonn

Author

Paul D. Hanna, Feb 04 2009

Status

approved