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A110313 E.g.f. exp(x)/(1-x-x^2). 2
1, 2, 7, 34, 221, 1786, 17347, 196442, 2542969, 37030546, 599172671, 10664259442, 207061905877, 4355429249354, 98661276360571, 2394559287772906, 61991654930903537, 1705178260099590562, 49662655090649112439 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,2

COMMENTS

Binomial transform of A005442. Rows sums of A039948.

LINKS

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

FORMULA

E.g.f.: exp(x)/(1-x-x^2).

a(n) = sum{k=0..n, binomial(n, k)*k!*F(k+1)}.

a(n) = sum{k=0..n, n!*F(n-k+1)/k!}.

Recurrence: 0=a(n+3)-(n+4)*a(n+2)-(n+2)^2*a(n+1)+(n+2)*(n+1)*a(n). [Emanuele Munarini, May 27 2011]

a(n) ~ n!*exp((sqrt(5)-1)/2)*((1+sqrt(5))/2)^(n+1)/sqrt(5). - Vaclav Kotesovec, Oct 18 2012

MATHEMATICA

Table[Sum[Binomial[n, k]k!Fibonacci[k + 1], {k, 0, n}], {n, 0, 100}] (* Emanuele Munarini, May 27 2011 *)

PROG

(Maxima) makelist(sum(binomial(n, k)*k!*fib(k+1), k, 0, n), n, 0, 19); [Emanuele Munarini, May 27 2011]

CROSSREFS

Cf. A000045.

Sequence in context: A049463 A294466 A029894 * A000944 A136310 A222868

Adjacent sequences:  A110310 A110311 A110312 * A110314 A110315 A110316

KEYWORD

easy,nonn

AUTHOR

Paul Barry, Jul 19 2005

STATUS

approved

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Last modified October 22 11:23 EDT 2018. Contains 316438 sequences. (Running on oeis4.)