A200380 Expansion of e.g.f. exp(x+x^2-1/6*x^3).

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

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!).

D-finite with recurrence 2*a(n) -2*a(n-1) +4*(-n+1)*a(n-2) +(n-1)*(n-2)*a(n-3)=0. - Bruno Berselli, Nov 17 2011

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 * A354017 A151396 A148604

Adjacent sequences: A200377 A200378 A200379 * A200381 A200382 A200383

Keyword

sign

Author

Vladimir Kruchinin, Nov 17 2011

Status

approved