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A144498 Column 2 of array in A144502. 6
1, 5, 30, 229, 2165, 24576, 326515, 4976315, 85630914, 1642623355, 34762642871, 804650577600, 20224019536825, 548535471681029, 15969883030969470, 496754110707779461, 16441934503725675485, 576991048929859964160, 21399021201104749243099, 836326710446071005267035 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

LINKS

Vincenzo Librandi, Table of n, a(n) for n = 0..200

FORMULA

E.g.f.: (1 - 2*x + 2*x*sqrt(1-2*x))*exp(1-sqrt(1-2*x))/(1-2*x)^2. - Sergei N. Gladkovskii, Oct 06 2012

G.f.: (1-x)/(x*Q(0)) - 1/x, where Q(k)= 1 - x - x*(k+1)/Q(k+1); (continued fraction). - Sergei N. Gladkovskii, May 18 2013

a(n) ~ 2^(n+3/2) * n^(n+1) / exp(n-1). - Vaclav Kotesovec, Oct 08 2013

G.f.: T(0)/x- 1/x, where T(k) = 1 - (k+1)*x/((k+1)*x - (1-x)^2/T(k+1) ); (continued fraction). - Sergei N. Gladkovskii, Nov 15 2013

MAPLE

f1:=proc(n) local k; add((n+k+1)!/((n-k)!*k!*2^k), k=0..n); end; [seq(f1(n), n=0..60)];

MATHEMATICA

Table[Sum[(n+k+1)!/((n-k)!*k!*2^k), {k, 0, n}], {n, 0, 20}] (* Vaclav Kotesovec, Oct 08 2013 *)

CROSSREFS

First differences of A001515 and A144301.

Sequence in context: A129695 A110521 A167892 * A201368 A072213 A257741

Adjacent sequences:  A144495 A144496 A144497 * A144499 A144500 A144501

KEYWORD

nonn

AUTHOR

David Applegate and N. J. A. Sloane, Dec 13 2008

STATUS

approved

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Last modified February 23 02:43 EST 2018. Contains 299473 sequences. (Running on oeis4.)