The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A334190 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A334190

a(n) = exp(1/2) * Sum_{k>=0} (2*k + 1)^n / ((-2)^k * k!).
(history; published version)

#8 by Susanna Cuyler at Sat Apr 18 11:49:38 EDT 2020

STATUS

proposed

approved

#7 by Vaclav Kotesovec at Sat Apr 18 10:39:05 EDT 2020

STATUS

editing

proposed

#6 by Vaclav Kotesovec at Sat Apr 18 10:38:42 EDT 2020

MATHEMATICA

Table[Sum[Binomial[n, k] * 2^k * BellB[k, -1/2], {k, 0, n}], {n, 0, 24}] (* Vaclav Kotesovec, Apr 18 2020 *)

STATUS

proposed

editing

#5 by Ilya Gutkovskiy at Sat Apr 18 09:33:56 EDT 2020

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Sat Apr 18 08:47:38 EDT 2020

CROSSREFS

Column k=2 of A334192.

#3 by Ilya Gutkovskiy at Sat Apr 18 08:38:50 EDT 2020

CROSSREFS

Cf. A007405, A009235, A293037, A308536, A334191.

#2 by Ilya Gutkovskiy at Sat Apr 18 08:34:20 EDT 2020

NAME

allocated for Ilya Gutkovskiy

a(n) = exp(1/2) * Sum_{k>=0} (2*k + 1)^n / ((-2)^k * k!).

DATA

1, 0, -2, -4, 4, 64, 248, 48, -6512, -51200, -171296, 830400, 17870400, 144684032, 441316224, -5976726784, -119879356160, -1123892297728, -3962230563328, 70410917051392, 1686366492509184, 19578100126072832, 101728414306826240, -1258662784047370240, -42727186269262737408

OFFSET

0,3

FORMULA

G.f.: (1/(1 - x)) * Sum_{k>=0} (-x/(1 - x))^k / Product_{j=1..k} (1 - 2*j*x/(1 - x)).

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

MATHEMATICA

nmax = 24; CoefficientList[Series[1/(1 - x) Sum[(-x/(1 - x))^k/Product[(1 - 2 j x/(1 - x)), {j, 1, k}], {k, 0, nmax}], {x, 0, nmax}], x]

nmax = 24; CoefficientList[Series[Exp[x + (1 - Exp[2 x])/2], {x, 0, nmax}], x] Range[0, nmax]!

CROSSREFS

Cf. A007405, A009235, A293037, A308536.

KEYWORD

allocated

sign

AUTHOR

Ilya Gutkovskiy, Apr 18 2020

STATUS

approved

editing

#1 by Ilya Gutkovskiy at Sat Apr 18 08:34:20 EDT 2020

NAME

allocated for Ilya Gutkovskiy

KEYWORD

allocated

STATUS

approved