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A202516 G.f.: exp( Sum_{n>=1} (2^n + 3^n)^n * x^n/n ). 1
1, 5, 97, 14735, 22208431, 314664801905, 41448076127290195, 50905029765702161210225, 582983891132858366160979787245, 62080074367851800086180277369110042475, 61205889017397342360456211893643596980919936577 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

More generally, for integers p and q, exp( Sum_{n>=1} (p^n + q^n)^n * x^n/n ) is a power series in x with integer coefficients.

LINKS

Table of n, a(n) for n=0..10.

EXAMPLE

G.f.: A(x) = 1 + 5*x + 97*x^2 + 14735*x^3 + 22208431*x^4 +...

where

log(A(x)) = (2+3)*x + (2^2 + 3^2)^2*x^2/2 + (2^3 + 3^3)^3*x^3/3 + (2^4 + 3^4)^4*x^4/4 + (2^5 + 3^5)^5*x^5/5 +...

more explicitly,

log(A(x)) = 5*x + 13^2*x^2/2 + 35^3*x^3/3 + 97^4*x^4/4 + 275^5*x^5/5 +...

PROG

(PARI) {a(n)=polcoeff(exp(sum(m=1, n, (2^m+3^m)^m*x^m/m)+x*O(x^n)), n)}

CROSSREFS

Cf. A202517, A155200, A155201, A155202.

Sequence in context: A102734 A117341 A295190 * A062538 A053980 A215299

Adjacent sequences:  A202513 A202514 A202515 * A202517 A202518 A202519

KEYWORD

nonn

AUTHOR

Paul D. Hanna, Dec 20 2011

STATUS

approved

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Last modified June 20 01:36 EDT 2019. Contains 324223 sequences. (Running on oeis4.)