The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A307259 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A307259

Expansion of (1/(1 - x)) * Product_{k>=1} (1 + k*x^k/(1 - x)^k).
(history; published version)

#9 by Bruno Berselli at Wed Apr 03 09:04:02 EDT 2019

STATUS

editing

approved

#8 by Paolo P. Lava at Wed Apr 03 05:14:54 EDT 2019

MAPLE

a:=series((1/(1-x))*mul(1+k*x^k/(1-x)^k, k=1..100), x=0, 31): seq(coeff(a, x, n), n=0..30); # Paolo P. Lava, Apr 03 2019

STATUS

approved

editing

#7 by Bruno Berselli at Tue Apr 02 05:37:27 EDT 2019

STATUS

reviewed

approved

#6 by Vaclav Kotesovec at Tue Apr 02 04:54:53 EDT 2019

STATUS

proposed

reviewed

#5 by Ilya Gutkovskiy at Mon Apr 01 11:22:33 EDT 2019

STATUS

editing

proposed

#4 by Ilya Gutkovskiy at Mon Apr 01 10:42:57 EDT 2019

CROSSREFS

Cf. A022629, A266232, A294502, A307260, A318127.

#3 by Ilya Gutkovskiy at Mon Apr 01 10:37:57 EDT 2019

NAME

allocated for Ilya Gutkovskiy

Expansion of (1/(1 - x)) * Product_{k>=1} (1 + k*x^k/(1 - x)^k).

DATA

1, 2, 5, 15, 44, 126, 357, 1003, 2783, 7618, 20627, 55421, 148021, 393140, 1038123, 2724992, 7112022, 18465708, 47726767, 122861732, 315123476, 805428727, 2051556778, 5207982062, 13177117709, 33235023381, 83574705456, 209576713721, 524181331710, 1307849984089, 3255539133109

OFFSET

0,2

COMMENTS

Binomial transform of A022629.

FORMULA

a(n) = Sum_{k=0..n} binomial(n,k)*A022629(k).

MATHEMATICA

nmax = 30; CoefficientList[Series[1/(1 - x) Product[(1 + k x^k/(1 - x)^k), {k, 1, nmax}], {x, 0, nmax}], x]

CROSSREFS

Cf. A022629, A266232, A294502, A318127.

KEYWORD

allocated

nonn

AUTHOR

Ilya Gutkovskiy, Apr 01 2019

STATUS

approved

editing

#2 by Ilya Gutkovskiy at Mon Apr 01 10:37:57 EDT 2019

NAME

allocated for Ilya Gutkovskiy

KEYWORD

recycled

allocated

#1 by Russ Cox at Sun Jan 27 08:30:53 EST 2019

KEYWORD

recycled

STATUS

approved