The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A131441 (Bold, blue-underlined text is an addition; faded, red-underlined text is a ~~deletion~~.)
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A131441

Row sums of triangle A130757 (coefficients of scaled Laguerre-Sonin polynomials n!(2^(n-m))*L(n,1/2,x)).
(history; published version)

#13 by Charles R Greathouse IV at Thu Sep 08 08:45:31 EDT 2022

PROG

(MAGMAMagma) [Round(Factorial(n)*(&+[(-1)^k*2^(n-k)*Gamma(n+3/2)/(Gamma(k+1) *Gamma(n -k+1)*Gamma(k+3/2)): k in [0..n]])): n in [0..20]]; // G. C. Greubel, May 14 2018

Discussion

Thu Sep 08

08:45

OEIS Server: https://oeis.org/edit/global/2944

#12 by Wesley Ivan Hurt at Sun Apr 17 22:19:52 EDT 2022

STATUS

editing

approved

#11 by Wesley Ivan Hurt at Sun Apr 17 22:19:45 EDT 2022

CROSSREFS

Cf. A130757.

STATUS

approved

editing

#10 by Susanna Cuyler at Tue May 15 08:36:23 EDT 2018

STATUS

proposed

approved

#9 by Michel Marcus at Tue May 15 00:59:01 EDT 2018

STATUS

editing

proposed

#8 by Michel Marcus at Tue May 15 00:58:58 EDT 2018

AUTHOR

Wolfdieter Lang , Aug 07 2007

STATUS

proposed

editing

#7 by G. C. Greubel at Tue May 15 00:39:19 EDT 2018

STATUS

editing

proposed

#6 by G. C. Greubel at Tue May 15 00:39:11 EDT 2018

LINKS

G. C. Greubel, <a href="/A131441/b131441.txt">Table of n, a(n) for n = 0..400</a>

FORMULA

a(n) = Sum_{m=sum(0..n} A130757(n,m),m=0..n), n>=0, with A130757(n,m) = n!*(2^(n-m)) *((-1)^m)*binomial(n+1/2,n-m)/m!, n>=m>=0, else 0.

MATHEMATICA

T[n_, k_]:= (-1)^k*n!*2^(n-k)*Binomial[n +1/2, n-k]/k!; Table[Sum[T[n, k], {k, 0, n}], {n, 0, 40}] (* G. C. Greubel, May 14 2018 *)

PROG

(PARI) for(n=0, 30, print1(sum(k=0, n, (-1)^k*n!*2^(n-k)*binomial(n+1/2, n-k)/k!), ", ")) \\ G. C. Greubel, May 14 2018

(MAGMA) [Round(Factorial(n)*(&+[(-1)^k*2^(n-k)*Gamma(n+3/2)/(Gamma(k+1) *Gamma(n -k+1)*Gamma(k+3/2)): k in [0..n]])): n in [0..20]]; // G. C. Greubel, May 14 2018

STATUS

approved

editing

#5 by R. J. Mathar at Wed Oct 02 15:12:36 EDT 2013

STATUS

proposed

approved

#4 by R. J. Mathar at Wed Oct 02 14:35:30 EDT 2013

STATUS

editing

proposed