OFFSET
0,3
LINKS
Eric Weisstein's World of Mathematics, Heptagonal Pyramidal Number
Index entries for linear recurrences with constant coefficients, signature (10,-45,120,-210,252,-210,120,-45,10,-1).
FORMULA
G.f.: x*(1 + 446*x + 10461*x^2 + 52420*x^3 + 75580*x^4 + 32544*x^5 + 3504*x^6 + 44*x^7)/(1 - x)^10.
a(n) = n *(5*n-2) *(n+1) *(5*n^3+3*n^2-2*n+6) *(25*n^3+15*n^2-10*n-12)/1296. - R. J. Mathar, Nov 28 2019
MATHEMATICA
Table[Sum[k (5 k - 3)/2, {k, 0, n (n + 1) (5 n - 2)/6}], {n, 0, 25}]
nmax = 25; CoefficientList[Series[x (1 + 446 x + 10461 x^2 + 52420 x^3 + 75580 x^4 + 32544 x^5 + 3504 x^6 + 44 x^7)/(1 - x)^10, {x, 0, nmax}], x]
LinearRecurrence[{10, -45, 120, -210, 252, -210, 120, -45, 10, -1}, {0, 1, 456, 14976, 181780, 1273970, 6293756, 24395756, 79119496, 223821235}, 26]
CROSSREFS
KEYWORD
nonn,easy
AUTHOR
Ilya Gutkovskiy, Nov 20 2019
STATUS
approved