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A200380 Expansion of e.g.f. exp(x+x^2-1/6*x^3). 0
1, 1, 3, 6, 21, 51, 201, 498, 2241, 4581, 26991, 17766, 359613, -995409, 6968781, -53627454, 259953921, -2292378327, 13839388731, -108459180954, 809434284741, -6158416812309, 50614251147153, -407335408369614, 3478999597913601, -30042633320442099, 266107969086122151 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..26.

FORMULA

a(n) = n!*sum(k=0..n, sum(j=0..k, binomial(j,n-3*k+2*j)*(-1)^(j-k)*6^(j-k)*binomial(k,j))/k!).

Conjecture:  a(n) = a(n-1)+2*(n-2)*a(n-2)-(1/2)*(n-3)*(n-2)*a(n-3). - Bruno Berselli, Nov 17 2011

MAPLE

a:=series(exp(x+x^2-1/6*x^3), x=0, 27): seq(n!*coeff(a, x, n), n=0..26); # Paolo P. Lava, Mar 27 2019

PROG

(Maxima) a(n):=n!*sum(sum(binomial(j, n-3*k+2*j)*(-1)^(j-k)*6^(j-k)*binomial(k, j), j, 0, k)/k!, k, 0, n);

CROSSREFS

Sequence in context: A124493 A136331 A063683 * A151396 A148604 A148605

Adjacent sequences:  A200377 A200378 A200379 * A200381 A200382 A200383

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Nov 17 2011

STATUS

approved

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Last modified June 24 00:21 EDT 2021. Contains 345403 sequences. (Running on oeis4.)