A174515 Expansion of g.f. exp( Sum_{n>=1} (2^n+3^n)^2*x^n/n ).

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).

Links

Stefano Spezia, Table of n, a(n) for n = 0..1000

Index entries for linear recurrences with constant coefficients, signature (25,-228,900,-1296).

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

Adjacent sequences: A174512 A174513 A174514 * A174516 A174517 A174518

Keyword

nonn,easy

Author

Paul D. Hanna, Apr 22 2010

Status

approved