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A181085 a(n) = Sum_{k=0..floor(n/2)} binomial(n-k,k)^(n+1) * n/(n-k). 2
1, 3, 25, 327, 6336, 513657, 142074241, 52903930911, 36806786795365, 148308705637730728, 1318954828711012426638, 15279013243159345043036553, 534104982404807772659968455891, 97749134742042348389685885848315523 (list; graph; refs; listen; history; text; internal format)
OFFSET
1,2
LINKS
EXAMPLE
L.g.f.: L(x) = x + 3*x^2/2 + 25*x^3/3 + 327*x^4/4 + 6336*x^5/5 + ...
which equals the series:
L(x) = (1 + x)*x + (1 + 2^4*x + x^2)*x^2/2
+ (1+ 3^5*x + 3^6*x^2 + x^3)*x^3/3
+ (1+ 4^6*x + 6^7*x^2 + 4^8*x^3 + x^4)*x^4/4
+ (1+ 5^7*x + 10^8*x^2 + 10^9*x^3 + 5^10*x^4 + x^5)*x^5/5
+ (1+ 6^8*x + 15^9*x^2 + 20^10*x^3 + 15^11*x^4 + 6^12*x^5 + x^6)*x^6/6 + ...
Exponentiation yields the g.f. of A181084:
exp(L(x)) = 1 + x + 2*x^2 + 10*x^3 + 92*x^4 + 1367*x^5 + 87090*x^6 + ...
MATHEMATICA
Table[Sum[Binomial[n-k, k]^(n+1)*(n/(n-k)), {k, 0, Floor[n/2]}], {n, 20}] (* G. C. Greubel, Apr 04 2021 *)
PROG
(PARI) a(n)=sum(k=0, n\2, binomial(n-k, k)^(n+1)*n/(n-k))
(PARI) {a(n)=n*polcoeff(sum(m=1, n, sum(k=0, m, binomial(m, k)^(m+k+1)*x^k)*x^m/m)+x*O(x^n), n)}
(Sage) [sum( binomial(n-k, k)^(n+1)*(n/(n-k)) for k in (0..n//2)) for n in (1..20)] # G. C. Greubel, Apr 04 2021
(Magma) [(&+[Binomial(n-j, j)^(n+1)*(n/(n-j)): j in [0..Floor(n/2)]]): j in [1..20]]; // G. C. Greubel, Apr 04 2021
CROSSREFS
Cf. A181084 (exp).
Sequence in context: A001907 A212722 A236268 * A143635 A246756 A023997
KEYWORD
nonn
AUTHOR
Paul D. Hanna, Oct 28 2010
STATUS
approved

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Last modified June 19 13:40 EDT 2024. Contains 373503 sequences. (Running on oeis4.)