The OEIS mourns the passing of Jim Simons and is grateful to the Simons Foundation for its support of research in many branches of science, including the OEIS.
login
The OEIS is supported by the many generous donors to the OEIS Foundation.

 

Logo
Hints
(Greetings from The On-Line Encyclopedia of Integer Sequences!)
A177826 Sub-triangle of A060187: even-indexed entries of even-indexed rows. 0
1, 1, 1, 1, 230, 1, 1, 10543, 10543, 1, 1, 331612, 4675014, 331612, 1, 1, 9116141, 906923282, 906923282, 9116141, 1, 1, 237231970, 121383780207, 743288515164, 121383780207, 237231970, 1, 1, 6031771195, 13342139253321, 342917527152507, 342917527152507, 13342139253321, 6031771195, 1, 1 (list; table; graph; refs; listen; history; text; internal format)
OFFSET
0,5
COMMENTS
Row sums are:{1, 2, 232, 21088, 5338240, 1832078848, 986530539520, 712531396354048,
686233400119951360, 838856713968361013248, 1275735509232452907827200,...}.
LINKS
EXAMPLE
{1},
{1, 1},
{1, 230, 1},
{1, 10543, 10543, 1},
{1, 331612, 4675014, 331612, 1},
{1, 9116141, 906923282, 906923282, 9116141, 1},
MATHEMATICA
p[x_, n_] = (1 - x)^(n + 1)*Sum[((2*k + 1)^n)*x^k, {k, 0, Infinity}];
t[n_, m_] := CoefficientList[FullSimplify[ExpandAll[p[x, n]]], x][[m + 1]];
Table[Table[t[n, 2*m], {m, 0, Floor[n/2]}], {n, 0, 20, 2}];
Flatten[%]
(*Alternative recursion for A060187*)
m = 2;
A[n_, 1] := 1
A[n_, n_] := 1
A[n_, k_] := A[n, k] = (m*n - m*k + 1)A[n - 1, k - 1] + (m*k - (m - 1))A[n - 1, k]
Table[A[n, k], {n, 10}, {k, n}]]
(* Alternative expansion for A060187*)
p[t_] = Exp[t] *x/(-Exp[2*t] + x)
Table[ CoefficientList[FullSimplify[ExpandAll[(n!*(-1 + x)^(n + \
1)/x)*SeriesCoefficient[ Series[p[t], {t, 0, 30}], n]]], x], {n, 0, 10}]
CROSSREFS
Sequence in context: A178673 A028452 A072020 * A122269 A171666 A321503
KEYWORD
nonn,tabl
AUTHOR
Roger L. Bagula, Dec 13 2010
STATUS
approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recents
The OEIS Community | Maintained by The OEIS Foundation Inc.

License Agreements, Terms of Use, Privacy Policy. .

Last modified June 13 00:21 EDT 2024. Contains 373362 sequences. (Running on oeis4.)