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A007347 Maximal Eulerian numbers of second kind.
(Formerly M1889)
9
1, 1, 2, 8, 58, 444, 4400, 58140, 785304, 12440064, 238904904, 4642163952, 101180433024, 2549865473424, 64728375139872, 1797171220690560, 56071264983487776, 1758073054805500608, 59321137058404865280, 2206689692993315764416, 82380712138316751438720 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

REFERENCES

R. L. Graham, D. E. Knuth and O. Patashnik, Concrete Mathematics. Addison-Wesley, Reading, MA, 1990, p. 256.

N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, Academic Press, 1995 (includes this sequence).

LINKS

Alois P. Heinz, Table of n, a(n) for n = 0..404

R. G. Wilson, V, Letter to N. J. A. Sloane, Apr. 1994

FORMULA

a(n) = max_{k=0..n} A201637(n, k). - Sean A. Irvine, Dec 28 2017

MAPLE

a:= n-> max(seq(combinat[eulerian2](n, k), k=0..n)):

seq(a(n), n=0..20);  # Alois P. Heinz, Dec 28 2017

PROG

(Python)

from sympy.core.cache import cacheit

@cacheit

def eulerian2(n, k): return 1 if k==0 else 0 if k==n else eulerian2(n - 1, k)*(k + 1) + eulerian2(n - 1, k - 1)*(2*n - k - 1)

def a(n): return max([eulerian2(n, k) for k in range(n+1)])

print(map(a, range(51))) # Indranil Ghosh, Dec 29 2017

CROSSREFS

Cf. A201637.

Sequence in context: A153553 A191481 A229529 * A185898 A063074 A319590

Adjacent sequences:  A007344 A007345 A007346 * A007348 A007349 A007350

KEYWORD

nonn

AUTHOR

N. J. A. Sloane, Mira Bernstein, Robert G. Wilson v

EXTENSIONS

More terms from Sean A. Irvine, Dec 28 2017

STATUS

approved

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Last modified November 17 18:48 EST 2018. Contains 317276 sequences. (Running on oeis4.)