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A097821
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Expansion of e.g.f. exp(2x)/(1-5x).
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1
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1, 7, 74, 1118, 22376, 559432, 16783024, 587405968, 23496238976, 1057330754432, 52866537722624, 2907659574746368, 174459574484786176, 11339872341511109632, 793791063905777690624, 59534329792933326829568
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OFFSET
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0,2
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COMMENTS
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Second binomial transform of n!*5^n.
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LINKS
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FORMULA
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a(n) = 5*n*a(n-1) + 2^n, n > 0, a(0)=1.
D-finite with recurrence a(n) +(-5*n-2)*a(n-1) +10*(n-1)*a(n-2)=0. - R. J. Mathar, Aug 20 2021
a(n) = 5^n * n! * Sum_{k = 0..n} (2/5)^k/k! = 5^n * exp(2/5) * gamma(n + 1, 2/5). - Gerry Martens, Nov 07 2022
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MAPLE
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f:= proc(n) option remember; 5*n*procname(n-1)+2^n end proc:
f(0):= 1:
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PROG
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(PARI) my(x='x + O('x^25)); Vec(serlaplace(exp(2*x)/(1-5*x))) \\ Michel Marcus, Nov 08 2022
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CROSSREFS
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KEYWORD
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easy,nonn
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AUTHOR
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STATUS
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approved
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