The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A365794

(Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
Showing entries 1-10 | older changes

A365794

Expansion of e.g.f. 1 / (3 - 2 * exp(2*x))^(3/4).
(history; published version)

#14 by Harvey P. Dale at Thu May 30 11:07:57 EDT 2024

STATUS

editing

approved

#13 by Harvey P. Dale at Thu May 30 11:07:50 EDT 2024

MATHEMATICA

With[{nn=20}, CoefficientList[Series[1/(3-2Exp[2x])^(3/4), {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, May 30 2024 *)

STATUS

approved

editing

#12 by Michael De Vlieger at Thu Nov 16 11:51:51 EST 2023

STATUS

proposed

approved

#11 by Seiichi Manyama at Thu Nov 16 09:22:59 EST 2023

STATUS

editing

proposed

#10 by Seiichi Manyama at Thu Nov 16 09:15:47 EST 2023

CROSSREFS

Cf. A365777, A365782.

#9 by Seiichi Manyama at Thu Nov 16 09:11:44 EST 2023

CROSSREFS

Cf. A365782.

#8 by Seiichi Manyama at Thu Nov 16 08:41:03 EST 2023

DATA

1, 3, 27, 369, 6849, 160803, 4566987, 152204769, 5822610849, 251445000483, 12098060349147, 641736701136369, 37204969609266849, 2340437711290748163, 158770522442243864907, 11553653430580844747169, 897732793887437892390849, 74182365989862425679675843

#7 by Seiichi Manyama at Thu Nov 16 08:40:27 EST 2023

PROG

(PARI) a(n) = sum(k=0, n, 2^(n-k)*prod(j=0, k-1, 4*j+3)*stirling(n, k, 2));

#6 by Seiichi Manyama at Thu Nov 16 07:47:31 EST 2023

FORMULA

a(n) = Sum_{k=0..n} 2^(n-k) * (Product_{j=0..k-1} (4*j+3)) * Stirling2(n,k).

a(0) = 1; a(n) = Sum_{k=1..n} 2^k * (2 - 1/2 * k/n) * binomial(n,k) * a(n-k).

a(0) = 1; a(n) = 3*a(n-1) - 3*Sum_{k=1..n-1} (-2)^k * binomial(n-1,k) * a(n-k).

#5 by Seiichi Manyama at Thu Nov 16 07:44:59 EST 2023

NAME

allocated for Seiichi Manyama

Expansion of e.g.f. 1 / (3 - 2 * exp(2*x))^(3/4).

DATA

1, 3, 27, 369, 6849, 160803, 4566987, 152204769, 5822610849, 251445000483, 12098060349147, 641736701136369, 37204969609266849, 2340437711290748163, 158770522442243864907

OFFSET

0,2

KEYWORD

allocated

nonn

AUTHOR

Seiichi Manyama, Nov 16 2023

STATUS

approved

editing