The On-Line Encyclopedia of Integer Sequences (OEIS)

Revision History for A162695

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A162695

E.g.f. satisfies A(x) = exp( x*A(x) * exp(x*A(x)) ).
(history; published version)

#15 by Alois P. Heinz at Wed Feb 08 11:11:16 EST 2023

STATUS

proposed

approved

#14 by Seiichi Manyama at Wed Feb 08 11:08:12 EST 2023

STATUS

editing

proposed

#13 by Seiichi Manyama at Wed Feb 08 11:06:58 EST 2023

PROG

(PARI) {a(n, m=1)=sum(k=0, n, binomial(n, k)*m*(n+m)^(k-1)*k^(n-k))};

{L(n)=if(n<1, 0, sum(k=1, n, binomial(n, k)*n^(k-1)*k^(n-k)))};

#12 by Seiichi Manyama at Wed Feb 08 11:03:06 EST 2023

FORMULA

a(n,m) = Sum_{k=0..n} Cbinomial(n,k) * m*(n+m)^(k-1) * k^(n-k).

L(n) = Sum_{k=0..n} Cbinomial(n,k) * n^(k-1) * k^(n-k) where

#11 by Seiichi Manyama at Wed Feb 08 11:00:16 EST 2023

NAME

E.g.f. satisfies: A(x) = exp( x*A(x) * exp(x*A(x)) ).

FORMULA

a(n) = Sum_{k=0..n} Cbinomial(n,k) * (n+1)^(k-1) * k^(n-k).

#10 by Seiichi Manyama at Wed Feb 08 10:59:59 EST 2023

LINKS

Seiichi Manyama, <a href="/A162695/b162695.txt">Table of n, a(n) for n = 0..361</a>

STATUS

approved

editing

#9 by R. J. Mathar at Tue Sep 27 12:41:24 EDT 2016

STATUS

editing

approved

#8 by R. J. Mathar at Tue Sep 27 12:41:20 EDT 2016

REFERENCES

R Lorentz, S Tringali, CH Yan, Generalized Goncarov polynomials, arXiv preprint arXiv:1511.04039, 2015

LINKS

R Lorentz, S Tringali, CH Yan, <a href="http://arxiv.org/abs/1511.04039">Generalized Goncarov polynomials</a>, arXiv preprint arXiv:1511.04039, 2015

STATUS

approved

editing

#7 by N. J. A. Sloane at Sat Aug 27 11:40:47 EDT 2016

STATUS

editing

approved

#6 by N. J. A. Sloane at Sat Aug 27 11:40:45 EDT 2016

REFERENCES

R Lorentz, S Tringali, CH Yan, Generalized Goncarov polynomials, arXiv preprint arXiv:1511.04039, 2015

STATUS

approved

editing