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A191470 E.g.f (1+arcsin(x))^arcsin(x) 0
1, 0, 2, -3, 28, -120, 1122, -8127, 88096, -885216, 11291624, -143432883, 2131731944, -32515910232, 555050034224, -9845456006487, 190381188822016, -3842126730651264, 83143449079579584, -1878918839085535971, 45029979676319086976 (list; graph; refs; listen; history; text; internal format)
OFFSET

0,3

LINKS

Table of n, a(n) for n=0..20.

FORMULA

a(n)=sum(m=1..n, sum(j=0..(n-m)/2, ((n-2*j)!*stirling1(n-m-2*j,m)*sum(k=0..2*j, (-1)^((3*k)/2)*binomial((n-2)/2,(2*j-k)/2)*sum(i=0..k,(2^i*stirling1(n-2*j+i,n-2*j)*binomial(n-2*j+k-1,n-2*j+i-1))/(n-2*j+i)!)))/(n-m-2*j)!)), n>0, a(0)=1.

MATHEMATICA

With[{nn=20}, CoefficientList[Series[(1+ArcSin[x])^ArcSin[x], {x, 0, nn}], x] Range[0, nn]!] (* Harvey P. Dale, Nov 19 2021 *)

PROG

(Maxima)

a(n):=sum(sum(((n-2*j)!*stirling1(n-m-2*j, m)*sum((-1)^((3*k)/2)*binomial((n-2)/2, (2*j-k)/2)*sum((2^i*stirling1(n-2*j+i, n-2*j)*binomial(n-2*j+k-1, n-2*j+i-1))/(n-2*j+i)!, i, 0, k), k, 0, 2*j))/(n-m-2*j)!, j, 0, (n-m)/2), m, 1, n);

CROSSREFS

Sequence in context: A037423 A009249 A012697 * A001094 A052848 A206592

Adjacent sequences:  A191467 A191468 A191469 * A191471 A191472 A191473

KEYWORD

sign

AUTHOR

Vladimir Kruchinin, Jun 03 2011

STATUS

approved

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Last modified January 24 00:05 EST 2022. Contains 350515 sequences. (Running on oeis4.)