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A372216
Product of n-th Pell number and n-th Catalan number: a(n) = A000129(n)*A000108(n).
0
1, 4, 25, 168, 1218, 9240, 72501, 583440, 4789070, 39940888, 337490426, 2883046320, 24858176900, 216046612080, 1890737146125, 16647522481440, 147365806700310, 1310740896927000, 11708311265437710, 104989351441019760
OFFSET
1,2
FORMULA
G.f.: 1/(2*x)-sqrt(sqrt(-16*x^2-8*x+1)+4*x+3)/(4*x).
D-finite with recurrence +n*(n+1)*a(n) -4*n*(2*n-1)*a(n-1) -4*(2*n-1)*(2*n-3)*a(n-2)=0. - R. J. Mathar, Apr 24 2024
MATHEMATICA
CoefficientList[Series[1/(2*x)-Sqrt[Sqrt[-16*x^2-8*x+1]+4*x+3]/(4*x), {x, 0, 20}], x] (* Stefano Spezia, Apr 22 2024 *)
CROSSREFS
Sequence in context: A357223 A074422 A128419 * A226945 A225137 A229255
KEYWORD
nonn
AUTHOR
Vladimir Kruchinin, Apr 22 2024
STATUS
approved