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 A245076 E.g.f.: Sum_{n>=0} exp(n*5^n*x) * x^n/n!. 3
 1, 1, 11, 226, 17001, 2671876, 1242300001, 1250703890626, 3363964848750001, 20117722302277734376, 302329590133667187500001, 10299774530356369019736328126, 846958190132982653045661328125001, 160085716663876329020695686381591796876 (list; graph; refs; listen; history; text; internal format)
 OFFSET 0,3 LINKS Vaclav Kotesovec, Asymptotic of sequences A244820, A244821 and A244822 FORMULA a(n) = Sum_{k=0..n} C(n,k) * k^(n-k) * 5^(k*(n-k)). O.g.f.: Sum_{n>=0} x^n/(1 - n*5^n*x)^(n+1). MATHEMATICA Flatten[{1, Table[Sum[Binomial[n, k]*k^(n-k)*5^(k*(n-k)), {k, 0, n}], {n, 1, 20}]}] PROG (PARI) {a(n) = sum(k=0, n, binomial(n, k) * k^(n-k) * 5^(k*(n-k)) )} for(n=0, 20, print1(a(n), ", ")) CROSSREFS Cf. A244820, A244821, A244822. Sequence in context: A281257 A187646 A170948 * A120850 A289716 A305141 Adjacent sequences:  A245073 A245074 A245075 * A245077 A245078 A245079 KEYWORD nonn,easy AUTHOR Vaclav Kotesovec, Jul 11 2014 STATUS approved

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Last modified August 20 22:45 EDT 2019. Contains 326155 sequences. (Running on oeis4.)