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A174515
Expansion of g.f. exp( Sum_{n>=1} (2^n+3^n)^2*x^n/n ).
1
1, 25, 397, 5125, 58813, 626725, 6356749, 62315125, 596370205, 5610245125, 52128987181, 480061573525, 4392455087677, 40002549209125, 363080219023693, 3287474035532725, 29714233445499229, 268240649382317125
OFFSET
0,2
COMMENTS
More generally, for integer m>=0 and real p and q,
exp( Sum_{n>=1} (p^n+q^n)^m*x^n/n ) = 1/Product_{k=0..m} (1 - p^k*q^(m-k)*x)^C(m,k).
FORMULA
O.g.f.: 1/((1-4*x)*(1-6*x)^2*(1-9*x)).
From Stefano Spezia, Jul 21 2022: (Start)
a(n) = 25*a(n-1) - 228*a(n-2) + 900*a(n-3) - 1296*a(n-4) for n > 3.
a(n) = (9^(2+n) - 4^(2+n) - 5*6^(1+n)*(2 + n))/5. (End)
PROG
(PARI) {a(n)=polcoeff(exp(sum(m=1, n+1, ((2^m+3^m)^2*x^m/m)+x*O(x^n))), n)}
CROSSREFS
Cf. A007689.
Sequence in context: A344733 A028130 A286719 * A028116 A028075 A042204
KEYWORD
nonn,easy
AUTHOR
Paul D. Hanna, Apr 22 2010
STATUS
approved